Search results for: ²¹⁰Pb dating method

Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: B. Chikh, L. Moussa, H. Bechtoula, Y. Mehani, A. Zerzour

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This study presents a new method, applicable to evaluation and design of structures has been developed and illustrated by comparison with the capacity spectrum method (CSM, ATC-40). This method uses inelastic spectra and gives peak responses consistent with those obtained when using the nonlinear time history analysis. Hereafter, the seismic demands assessment method is called in this paper DSM, Ductility Spectrum Method. It is used to estimate the seismic deformation of Single-Degree-Of-Freedom (SDOF) systems based on DDRS, Ductility Demand Response Spectrum, developed by the author.

Keywords: seismic demand, capacity, inelastic spectra, design and structure

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Authors: Stamataki Erofili Nellie, Benardos Andreas

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Winemaking and aging in Greece has been performed so far in special facilities, designed either as above ground or shallow underground buildings. The latter are well-known in Santorini as “canaves,” dating back to the 1700s. Canaves were mainly used for wine storage and aging, although occasionally, they included a winepress to complete there the whole wine production. On the other hand, wine caves are subterranean caves of the same use as canaves in the wine manufacturing industry, but they are excavated at a much greater depth of more than 53 meters or 175 feet. Whereas canaves or a typical wine cellar is around 10 feet deep, with is equivalent to almost 3 meters. This paper discusses the advantages and the disadvantages of creating a wine cave for the vinification of a winery in Greece and the financial investment or risk that has to be taken. The data presented and analysed are given from wineries in Greece and especially from those located in Santorini island. The estimation of the cost for the excavation of the model selected as a wine cave will be compared with the financial budget of the existing premises and facilities above ground in Greek wineries. In order to show whether it is viable for a greek winery to invest in a wine cave.

Keywords: underground space use, subterranean winery, wine cave, underground winery, greece

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Authors: Saheed A. Gbadegeshin

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Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.

Keywords: commercialization method, technology, knowledge, intellectual property, innovation, invention

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Authors: Aicha Zohbie

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The purpose of this paper is to critically compare two teaching methods: the communicative method and the grammar-translation method. The paper presents the importance of language awareness as an approach to teaching and learning language and some challenges that language teachers face. In addition, the paper strives to determine whether the adoption of communicative teaching methods or the grammar teaching method would be more effective to teach a language. A variety of features are considered for comparing the two methods: the purpose of each method, techniques used, teachers’ and students’ roles, the use of L1, the skills that are emphasized, the correction of students’ errors, and the students’ assessments. Finally, the paper includes suggestions and recommendations for implementing an approach that best meets the students’ needs in a classroom.

Keywords: language teaching methods, language awareness, communicative method grammar translation method, advantages and disadvantages

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.

Keywords: cable ampacity, finite element method, underground cable, thermal rating

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: drape, drape shape, automated drapemeter, fabric

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Authors: Elmira Aliyeva, Dadash Huseynov, Robert Hoogendoorn, Salomon Kroonenberg

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The Kura River is the major water artery in the Southern Caucasus; it is a third river in the Caspian Sea basin in terms of length and size of the catchment area, the second in terms of the water budget, and the first in the volume of sediment load. Understanding of major controls on the Kura fluvial- deltaic system is valuable for efficient management of the highly populated river basin and coastal zone. We have studied grain size of sediments accumulated in the river channels and delta and dated by 210Pb method, astrophotographs, old topographic and geological maps, and archive data. At present time sediments are supplied by the Kura River to the Caspian Sea through three distributary channels oriented north-east, south-east, and south-west. The river is dominated by the suspended load - mud, silt, very fine sand. Coarse sediments are accumulated in the distributaries, levees, point bar, and delta front. The annual suspended sediment budget in the time period 1934-1952 before construction of the Mingechavir water reservoir in 1953 in the Kura River midstream area was 36 mln.t/yr. From 1953 to 1964, the suspended load has dropped to 12 mln.t/yr. After regulation of the Kura River discharge the volume of suspended load transported via north-eastern channel reduced from 35% of the total sediment amount to 4%, and through the main south-eastern channel increased from 65% to 96% with further fall to 56% due to creation of new south-western channel in 1964. Between 1967-1976 the annual sediment budget of the Kura River reached 22,5 mln. t/yr. From 1977 to 1986, the sediment load carried by the Kura River dropped to 17,6 mln.t/yr. The historical data show that between 1860 and 1907, during relatively stable Caspian Sea level two channels - N and SE, appear to have distributed an equal amount of sediments as seen from the bilateral geometry of the delta. In the time period 1907-1929, two new channels - E and NE, appeared. The growth of three delta lobes - N, NE, and SE, and rapid progradation of the delta has occurred on the background of the Caspian Sea level rise as a result of very high sediment supply. Since 1929 the Caspian Sea level decline was followed by the progradation of the delta occurring along the SE channel. The eastern and northern channels have been silted up. The slow rate of progradation at its initial stage was caused by the artificial reduction in the sediment budget. However, the continuous sea-level fall has brought to this river bed gradient increase, high erosional rate, increase in the sediment supply, and more rapid progradation. During the subsequent sea-level rise after 1977 accompanied by the decrease in the sediment budget, the southern part of the delta has turned into a complex of small, shallow channels oriented to the south. The data demonstrate that behaviour of the Kura fluvial – deltaic system and variations in the sediment budget besides anthropogenic regulation are strongly governed by the Caspian Sea level very rapid changes.

Keywords: anthropogenic control on sediment budget, Caspian sea-level variations, Kura river sediment load, morphology of the Kura river delta, sedimentation in the Kura river delta

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Authors: Robert D. Hanser, Gina M. Hanser

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This paper provides an overview of Coordinated Community Response Teams (CCRT) to Intimate Partner Violence (IPV). The CCRT, as a partnership and collaborative effort between multiple agencies is highlighted. This paper is a legal analysis that showcases new legislation and legal requirements in the United States for investigating, processing, and reporting to acts of victimization have transformed the role of the university’s CCRT on campus, making its mission all the more important, both internal and external to the campus. As a specific example, discussion of the CCRT in Northeast Louisiana at the University of Louisiana at Monroe is provided as an example of involvement in this initiative, where federal grant funding has allowed a micro version of the region’s CCRT to be implemented on that campus. Simultaneously, university personnel also work with external agencies throughout the community in intimate partner violence response. Amidst this, the result is a genuine partnership between practitioners and researchers who work together to provide public awareness, prevention, first-responder, and intervention services in a comprehensive manner throughout Northeast Louisiana.

Keywords: interperaonal violence, sexual assault, dating violence, campus violence

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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

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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: 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: David Shengelia, Tamara Tsutsunava, Manana Togonidze, Giorgi Chichinadze, Giorgi Beridze

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Orthoclase gabbro intrusive exposes in the Eastern part of the Dzirula crystalline massif of the Central Transcaucasian microcontinent. It is intruded in the Baikal quartz-diorite gneisses as a stock-like body. The intrusive is characterized by heterogeneity of rock composition: variability of mineral content and irregular distribution of rock-forming minerals. The rocks are represented by pyroxenites, gabbro-pyroxenites and gabbros of different composition – K-feldspar, pyroxene-hornblende and biotite bearing varieties. Scientific views on the genesis and age of the orthoclase gabbro intrusive are considerably different. Based on the long-term pertogeochemical and geochronological investigations of the intrusive with such an extraordinary composition the authors came to the following conclusions. According to geological and geophysical data, it is stated that in the Saurian orogeny horizontal tectonic layering of the Earth’s crust of the Central Transcaucasian microcontinent took place. That is precisely this fact that explains the formation of the orthoclase gabbro intrusive. During the tectonic doubling of the Earth’s crust of the mentioned microcontinent thick tectonic nappes of mafic and sialic layers overlap the sialic basement (‘inversion’ layer). The initial magma of the intrusive was of high-temperature basite-ultrabasite composition, crystallization products of which are pyroxenites and gabbro-pyroxenites. Petrochemical data of the magma attest to its formation in the Upper mantle and partially in the ‘crustal astenolayer’. Then, a newly formed overheated dry magma with phenocrysts of clinopyrocxene and basic plagioclase intruded into the ‘inversion’ layer. From the new medium it was enriched by the volatile components causing the selective melting and as a result the formation of leucocratic quartz-feldspar material. At the same time in the basic magma intensive transformation of pyroxene to hornblende was going on. The basic magma partially mixed with the newly formed acid magma. These different magmas intruded first into the allochthonous basite layer without its significant transformation and then into the upper sialic layer and crystallized here at a depth of 7-10 km. By petrochemical data the newly formed leucocratic granite magma belongs to the S type granites, but the above mentioned mixed magma – to H (hybrid) type. During the final stage of magmatic processes the gabbroic rocks impregnated with high-temperature feldspar-bearing material forming anorthoclase or orthoclase. Thus, so called ‘orthoclase gabbro’ includes the rocks of various genetic groups: 1. protolith of gabbroic intrusive; 2. hybrid rock – K-feldspar gabbro and 3. leucocratic quartz-feldspar bearing rock. Petrochemical and geochemical data obtained from the hybrid gabbro and from the inrusive protolith differ from each other. For the identification of petrogenetic model of the orthoclase gabbro intrusive formation LA-ICP-MS- U-Pb zircon dating has been conducted in all three genetic types of gabbro. The zircon age of the protolith – mean 221.4±1.9 Ma and of hybrid K-feldspar gabbro – mean 221.9±2.2 Ma, records crystallization time of the intrusive, but the zircon age of quartz-feldspar bearing rocks – mean 323±2.9 Ma, as well as the inherited age (323±9, 329±8.3, 332±10 and 335±11 Ma) of hybrid K-feldspar gabbro corresponds to the formation age of Late Variscan granitoids widespread in the Dzirula crystalline massif.

Keywords: The Caucasus, isotope dating, orthoclase-bearing gabbro, petrogenetic model

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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: 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: 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: Alkaben Patel

Abstract:

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: Jorge Martinez-Garcia, Ingrid Stelzner, Joerg Stelzner, Damian Gwerder, Philipp Schuetz

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Tree-ring analysis is an important part of the quality assessment and the dating of (archaeological) wood samples. It provides quantitative data about the whole anatomical ring structure, which can be used, for example, to measure the impact of the fluctuating environment on the tree growth, for the dendrochronological analysis of archaeological wooden artefacts and to estimate the wood mechanical properties. Despite advances in computer vision and edge recognition algorithms, detection and counting of annual rings are still limited to 2D datasets and performed in most cases manually, which is a time consuming, tedious task and depends strongly on the operator’s experience. This work presents an image processing approach to detect the whole 3D tree-ring structure directly from X-ray computed tomography imaging data. The approach relies on a modified Canny edge detection algorithm, which captures fully connected tree-ring edges throughout the measured image stack and is validated on X-ray computed tomography data taken from six wood species.

Keywords: ring recognition, edge detection, X-ray computed tomography, dendrochronology

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Authors: Naman Solanki, Souraj Mondal

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With the world moving towards online communication, the video datastore has exploded in the past few years. Consequently, it has become crucial to analyse participant’s engagement levels in online communication videos. Engagement prediction of people in videos can be useful in many domains, like education, client meetings, dating, etc. Video-level or frame-level prediction of engagement for a user involves the development of robust models that can capture facial micro-emotions efficiently. For the development of an engagement prediction model, it is necessary to have a widely-accepted standard dataset for engagement analysis. DAiSEE is one of the datasets which consist of in-the-wild data and has a gold standard annotation for engagement prediction. Earlier research done using the DAiSEE dataset involved training and testing standard models like CNN-based models, but the results were not satisfactory according to industry standards. In this paper, a multi-level classification approach has been introduced to create a more robust model for engagement analysis using the DAiSEE dataset. This approach has recorded testing accuracies of 0.638, 0.7728, 0.8195, and 0.866 for predicting boredom level, engagement level, confusion level, and frustration level, respectively.

Keywords: computer vision, engagement prediction, deep learning, multi-level classification

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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: 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

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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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