Search results for: drying method

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Chui Ka Shing

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This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.

Keywords: bar model method, curriculum development, mathematics education, problem solving

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Azizakhanim Maharramli

Abstract:

The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

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Authors: Mahacine Amrani

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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Joseph Kimutai Langat

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Tea typology is the science of classifying tea. This study was carried out between November 2023 and July 2024, whose main objective was to investigate the typological classification nomenclature of processed tea in the world, narrowing down to Kenya. Centres of origin, historical background, tea growing region, scientific naming system, market, fermentation levels, processing/ oxidation levels and cultural reasons are used to classify tea at present. Of these, the most common typology is by oxidation, and more specifically, by the production methods within the oxidation categories. While the Asian tea producing countries categorises tea products based on the decreasing oxidation levels during the manufacturing process: black tea, green tea, oolong tea and instant tea, Kenya’s tea typology system is based on the degree of fermentation process, i.e. black tea, purple tea, green tea and white tea. Tea is also classified into five categories: black tea, green tea, white tea, oolong tea, and dark tea. Black tea is the main tea processed and exported in Kenya, manufactured mainly by withering, rolling, or by use of cutting-tearing-curling (CTC) method that ensures efficient conversion of leaf herbage to made tea, oxidizing, and drying before being sorted into different grades. It is from these varied typological methods that this review paper concludes that different regions of the world use different classification nomenclature. Therefore, since tea typology is not standardized, it is recommended that a global tea regulator dealing in tea classification be created to standardize tea typology, with domestic in-country regulatory bodies in tea growing countries accredited to implement the global-wide typological agreements and resolutions.

Keywords: classification, fermentation, oxidation, tea, typology

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Authors: Wu Peiqin

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Flexible thermoelectric devices are light and flexible, which can be in close contact with any shape of heat source surfaces to minimize heat loss and achieve efficient energy conversion. Among the wide application fields, energy harvesting via flexible thermoelectric generators can adapt to a variety of curved heat sources (such as human body, circular tubes, and surfaces of different shapes) and can drive low-power electronic devices, exhibiting one of the most promising technologies in self-powered systems. The heat flux along the cross-section of the flexible thin-film generator is limited by the thickness, so the temperature difference decreases during the generation process, and the output power is low. At present, most of the heat flow directions of the thin film thermoelectric generator are along the thin-film plane; however, this method is not suitable for attaching to the human body surface to generate electricity. In order to make the film generator more suitable for thermoelectric generation, it is necessary to apply a flexible heatsink on the air sides with the film to maintain the temperature difference. In this paper, Bismuth telluride thermoelectric paste was deposited on polyimide flexible substrate by a screen printing method, and the flexible thermoelectric film was formed after drying. There are ten pairs of thermoelectric legs. The size of the thermoelectric leg is 20 x 2 x 0.1 mm, and adjacent thermoelectric legs are spaced 2 mm apart. A phase change material-based flexible heatsink was designed and fabricated. The flexible heatsink consists of n-octadecane, polystyrene, and expanded graphite. N-octadecane was used as the thermal storage material, polystyrene as the supporting material, and expanded graphite as the thermally conductive additive. The thickness of the flexible phase change material-based heatsink is 2mm. A thermoelectric performance testing platform was built, and its output performance was tested. The results show that the system can generate an open-circuit output voltage of 3.89 mV at a temperature difference of 10K, which is higher than the generator without a heatsink. Therefore, the flexible heatsink can increase the temperature difference between the two ends of the film and improve the output performance of the flexible film generator. This result promotes the application of the film thermoelectric generator in collecting human heat for power generation.

Keywords: flexible thermoelectric generator, screen printing, PCM, flexible heatsink

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Authors: Jiankang Wang, Hongyang Yu

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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Ihsan Burak Cam, Ayhan Topuz

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Turkish delight has been produced by bleaching the plain delight mix (refined sugar, water and starch) via soapwort extract and powdered sugar. Soapwort extract which contains high amount of saponin, is an additive used in Turkish delight and tahini halvah production to improve consistency, chewiness and color due to its bioactive saponin content by acting as emulsifier. In this study, soapwort powder has been produced by determining optimum process conditions of soapwort extract by using response-surface method. This extract has been enriched with saponin by reverse osmosis (contains %63 saponin in dry bases). Büchi mini spray dryer B-290 was used to produce spray-dried soapwort powder (aw=0.254) from the enriched soapwort concentrate. Processing steps optimization and saponin content enrichment of soapwort extract has been tested on Turkish Delight production. Delight samples, produced by soapwort powder and commercial extract (control), were compared in chewiness, springiness, stickiness, adhesiveness, hardness, color and sensorial characteristics. According to the results, all textural properties except hardness of delights produced by powder were found to be statistically different than control samples. Chewiness, springiness, stickiness, adhesiveness and hardness values of samples (delights produced by the powder / control delights) were determined to be 361.9/1406.7, 0.095/0.251, -120.3/-51.7, 781.9/1869.3, 3427.3g/3118.4g, respectively. According to the quality analysis that has been ran with the end products it has been determined that; there is no statistically negative effect of the soapwort extract and the soapwort powder on the color and the appearance of Turkish Delight.

Keywords: saponin, delight, soapwort powder, spray drying

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: Sajia Islam, T. Tahsina, S. Raihana, M. M. Rahman, Q. S. Rahman, T. M. Huda, S. E. Arifeen, M. J. Dibley

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Early neonatal sepsis accounts for more than two-thirds of all deaths in the first year of life. This study assessed the counseling during antenatal, perinatal, post natal periods and its association with possible sepsis in rural Bangladesh. Method: Data were collected from a large community-based trial in Bangladesh where pregnant women were enrolled from 2013-2015 covering 29,497 newborns. Sepsis was defined using neonatal danger signs reported by 'The Young-Infants Clinical Science Study Group. 'Result: Signs of sepsis was found among 15% of the neonates. Neonatal sepsis was higher among those who did not receive advice on TT vaccinations (15.4% vs. 11%, p < 0.05) and danger signs (14.8% vs. 12.8%, p < 0.05) during pregnancy. Advice on delivering in well-lit place was significantly associated with lower incidence of sepsis (12.7% vs. 14.8% p < 0.05). Sepsis was lower among neonates whose mothers were counseled on immediate newborn care for bathing after 3 days of delivery (13.4% vs. 15.2% p=0), breastfeeding within 1hr of birth (13.82 % vs. 15.28% p=0), apply nothing on the cord (11.54 vs. 15.06 p=0), immediate drying of child (12.62% vs. 14.89%, p=0). Neonatal sepsis was lower among children whose mothers received 2-4 advice [OR=0.91(95% CI: 0.85-0.97)] compared to neonates whose mothers received only 1 or none. Overall, children to mothers who received ≥ 5 advice had lowest incidence of sepsis [OR=0.83 (95% CI: 0.71-0.97)] Conclusion: Advice on antenatal, prenatal and post natal is significantly reduced with early newborn sepsis. Further research is required to identify specific type of counseling messages that translate into practices and reduce pathways towards early-newborn morbidities.

Keywords: ante natal care, counseling, neonatal sepsis, post natal care

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Bolatbek Rysbaiuly, Nazerke Rysbayeva, Aigerim Rysbayeva

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Relevance: Energy saving elevated to public policy in almost all developed countries. One of the areas for energy efficiency is improving and tightening design standards. In the tie with the state standards, make high demands for thermal protection of buildings. Constructive arrangement of layers should ensure normal operation in which the humidity of materials of construction should not exceed a certain level. Elevated levels of moisture in the walls can be attributed to a defective condition, as moisture significantly reduces the physical, mechanical and thermal properties of materials. Absence at the design stage of modeling the processes occurring in the construction and predict the behavior of structures during their work in the real world leads to an increase in heat loss and premature aging structures. Method: To solve this problem, widely used method of mathematical modeling of heat and mass transfer in materials. The mathematical modeling of heat and mass transfer are taken into the equation interconnected layer [1]. In winter, the thermal and hydraulic conductivity characteristics of the materials are nonlinear and depends on the temperature and moisture in the material. In this case, the experimental method of determining the coefficient of the freezing or thawing of the material becomes much more difficult. Therefore, in this paper we propose an approximate method for calculating the thermal conductivity and moisture permeability characteristics of freezing or thawing material. Questions. Following the development of methods for solving the inverse problem of mathematical modeling allows us to answer questions that are closely related to the rational design of fences: Where the zone of condensation in the body of the multi-layer fencing; How and where to apply insulation rationally his place; Any constructive activities necessary to provide for the removal of moisture from the structure; What should be the temperature and humidity conditions for the normal operation of the premises enclosing structure; What is the longevity of the structure in terms of its components frost materials. Tasks: The proposed mathematical model to solve the following problems: To assess the condition of the thermo-physical designed structures at different operating conditions and select appropriate material layers; Calculate the temperature field in a structurally complex multilayer structures; When measuring temperature and moisture in the characteristic points to determine the thermal characteristics of the materials constituting the surveyed construction; Laboratory testing to significantly reduce test time, and eliminates the climatic chamber and expensive instrumentation experiments and research; Allows you to simulate real-life situations that arise in multilayer enclosing structures associated with freezing, thawing, drying and cooling of any layer of the building material.

Keywords: energy saving, inverse problem, heat transfer, multilayer walling

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Authors: Norliza Saparin, Ahmadilfitri Noor, Mohd Suria Affandi Yusoff, Shawaluddin Tahiruddin

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A palm oil mill produces crude palm oil (CPO) and has many operation units that comprises of sterilization, stripping, digestion and pressing, clarification, purification, drying and storage. This study investigated the total chlorine in palm fruit and CPO after each operating units. The total chlorine were determined by Mitsubishi NSX-2100 H, Trace Elemental Analyzer. The trace elemental analyzer is a furnace system with a micro-coulometric detector that was used for measuring and detecting total chlorine whether in organic or inorganic form. This determination is important as the chlorine is a direct precursor for 3-MCPD ester.

Keywords: chlorine, micro-coulometric, palm oil, 3-MCPD

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: Keiji Komatsu, Hayato Maruyama, Ariyuki Kato, Atsushi Nakamura, Shigeo Ohshio, Hiroki Akasaka, Hidetoshi Saitoh

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Violet Sr–Al–O:Eu2+ phosphor particles were synthesized from a metal–ethylenediaminetetraacetic acid (EDTA) solution of Sr, Al, Eu, and particulate alumina via spray drying and sintering in a reducing atmosphere. The crystal structures and emission properties at 85–300 K were investigated. The composition of the violet Sr–Al–O:Eu2+ phosphor particles was determined from various Sr–Al–O:Eu2+ phosphors by their emission properties’ dependence on temperature. The highly crystalline SrAl12O19:Eu2+ emission phases were confirmed by their crystallite sizes and the activation energies for the 4f5d–8S7/2 transition of the Eu2+ ion. These results showed that the material identification for the violet Sr–Al–O:Eu2+ phosphor was accomplished by the low-temperature luminescence measurements.

Keywords: low temperature luminescence spectroscopy, material identification, strontium aluminates phosphor, emission properties

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Authors: Adebola Ajayi

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Ocimum gratissimum belongs to the Lamiaceae family and is know generally as African Basil. Ocimum gratissimum leaves are widely used as local condiments in diets. The leaves were destalked sorted, washed with potable water to remove dirts, air dried for 14 days under ambient temperature and milled into powder. The proximate composition and mineral contents of Ocimum gratissimum leaves were investigated. The proximate analysis showed the moisture, crude, protein, total ash, crude fiber, crude lipid and total carbohydrate contents were 10.72±0.01%, 12.98±0.10%, 10.95±0.42, 10.21±0.04%, 4.81±0.04% and 49.01±0.25% respectively. The results of the analysis showed that Ocimum gratissimum could be a good source of important food nutrients.

Keywords: African Basil, drying, Ocimum gratissimum, proximate

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Sahar El Kasmi, Ayoub Aziz, Saadia Lharti, Mohammed El Janati, Boubker Boukili, Nacer El Motawakil, Mayom Chol Luka Awan

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Two types of geomaterials (Red Triassic clay from the Maaziz region and Yellow Pliocene clay from the Akrach region) were used to create different mixtures for the fabrication of ceramic bricks. This study investigated the influence of the Pliocene clay on the overall composition and mechanical properties of the Triassic clay. The red Triassic clay, sourced from Maaziz, underwent various mechanical processes and treatments to facilitate its transformation into ceramic bricks for construction. The triassic clay was subjected to a drying chamber and a heating chamber at 100°C to remove moisture. Subsequently, the dried clay samples were processed using a Planetary Babs ll Mill to reduce particle size and improve homogeneity. The resulting clay material was sieved, and the fine particles below 100 mm were collected for further analysis. In parallel, the Miocene marl obtained from the Akrach region was fragmented into finer particles and subjected to similar drying, grinding, and sieving procedures as the triassic clay. The two clay samples are then amalgamated and homogenized in different proportions. Precise measurements were taken using a weighing balance, and mixtures of 90%, 80%, and 70% Triassic clay with 10%, 20%, and 30% yellow clay were prepared, respectively. To evaluate the impact of Pliocene marl on the composition, the prepared clay mixtures were spread evenly and treated with a water modifier to enhance plasticity. The clay was then molded using a brick-making machine, and the initial manipulation process was observed. Additional batches were prepared with incremental amounts of Pliocene marl to further investigate its effect on the fracture behavior of the clay, specifically their resistance. The molded clay bricks were subjected to compression tests to measure their strength and resistance to deformation. Additional tests, such as water absorption tests, were also conducted to assess the overall performance of the ceramic bricks fabricated from the different clay mixtures. The results were analyzed to determine the influence of the Pliocene marl on the strength and durability of the Triassic clay bricks. The results indicated that the incorporation of Pliocene clay reduced the fracture of the triassic clay, with a noticeable reduction observed at 10% addition. No fractures were observed when 20% and 30% of yellow clay are added. These findings suggested that yellow clay can enhance the mechanical properties and structural integrity of red clay-based products.

Keywords: triassic clay, pliocene clay, mineralogical composition, geo-materials, ceramics, akach region, maaziz region, morocco.

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Authors: Mei-Jie Xu, Yang Zhong

Abstract:

Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Ekaterina Artiukhina, Panagiotis Grammelis

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Torrefaction of biomass pellets is considered as a useful pretreatment technology in order to convert them into a high quality solid biofuel that is more suitable for pyrolysis, gasification, combustion and co-firing applications. In the course of torrefaction the temperature varies across the pellet, and therefore chemical reactions proceed unevenly within the pellet. However, the uniformity of the thermal distribution along the pellet is generally assumed. The torrefaction process of a single cylindrical pellet is modeled here, accounting for heat transfer coupled with chemical kinetics. The drying sub-model was also introduced. The non-stationary process of wood pellet decomposition is described by the system of non-linear partial differential equations over the temperature and mass. The model captures well the main features of the experimental data.

Keywords: torrefaction, biomass pellets, model, heat, mass transfer

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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