Search results for: weight method

Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: Zasiah Tafheem, Mahadee Hasan Shourav, Zahidul Islam, Saima Islam Tumpa

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The paper aims at investigating the effect of number of story on different structural components of reinforced concrete building due to gravity and lateral loading. For the study, three building models having same building plan of three, six and nine stories are analyzed and designed using software package. All the buildings are residential and are located in Dhaka city of Bangladesh. Lateral load including wind and earthquake loading are applied to the building along both longitudinal and transverse direction as per Bangladesh National Building Code (BNBC, 2006). Equivalent static force method is followed for the applied seismic loading. The present study investigates as well as compares mainly total steel requirement in different structural components for those buildings. It has been found that total longitudinal steel requirement for beams at each floor is 48.57% for three storied building, 61.36% for six storied building when the total percentage is taken as 100% in case of nine storied building. For an exterior column, the steel ratio is 2.1%, 3.06%, 4.55% for three, six and nine storied building respectively for the first three floors. In addition, it has been noted that total weight of longitudinal reinforcement of an interior column is 14.02 % for threestoried building and 43.12% for six storied building when the total reinforcement is considered 100% for nine storied building for the first three floors.

Keywords: Equivalent Static Force Method, longitudinal reinforcement, seismic loading, steel ratio.

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Authors: A. Galashev

Abstract:

Absorption spectra of infra-red (IR) radiation of the disperse water medium absorbing the most important greenhouse gases: CO2 , N2O , CH4 , C2H2 , C2H6 have been calculated by the molecular dynamics method. Loss of the absorbing ability at the formation of clusters due to a reduction of the number of centers interacting with IR radiation, results in an anti-greenhouse effect. Absorption of O3 molecules by the (H2O)50 cluster is investigated at its interaction with Cl- ions. The splitting of ozone molecule on atoms near to cluster surface was observed. Interaction of water cluster with Cl- ions causes the increase of integrated intensity of emission spectra of IR radiation, and also essential reduction of the similar characteristic of Raman spectrum. Relative integrated intensity of absorption of IR radiation for small water clusters was designed. Dependences of the quantity of weight on altitude for vapor of monomers, clusters, droplets, crystals and mass of all moisture were determined. The anti-greenhouse effect of clusters was defined as the difference of increases of average global temperature of the Earth, caused by absorption of IR radiation by free water molecules forming clusters, and absorption of clusters themselves. The greenhouse effect caused by clusters makes 0.53 K, and the antigreenhouse one is equal to 1.14 K. The increase of concentration of CO2 in the atmosphere does not always correlate with the amplification of greenhouse effect.

Keywords: Greenhouse gases, infrared absorption and Raman spectra, molecular dynamics method, water clusters.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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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, simulation.

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Authors: Behnam Shirkhanghah, Ali Darabadi-Zare, Houshyar Eimani-Kalesar, Babak Pahlevan

Abstract:

Prestressing in structure increases ratio of load-bearing capacity to weight. Suspendomes are single-layer braced domes reinforced with cable and strut. Prestressing of cables alter value and distribution of stress in structure. In this study two configuration, diamatic and lamella domes is selected. Investigated domes have span of 100m with rise-to-span ratios of 0.1, 0.2, and 0.3. Single layer domes loaded under service load combinations according to ISO code. After geometric nonlinear analysis, models are designed with tubular and I-shaped sections then reinforced with cable and strut and converted to suspendomes. Displacements and stresses of some groups of nodes and elements in all of single-layer domes and suspendomes for three load combinations, symmetric snow, asymmetric snow and wind are compared. Variation due to suspending system is investigated. Suspendomes are redesigned and minimum possible weight after addition of cable and strut is obtained.

Keywords: Braced dome, Prestressing, Single-layer, Suspendome.

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Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: A. Soltani, M. Karimi Demneh

Abstract:

In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Wael M. Semida, P. Hadley, W. Sobeih, N. A. El-Sawah, M. A. S. Barakat

Abstract:

Photoselective plastic films with thermic properties are now available so that greenhouses clad with such plastics exhibit a higher degree of “Greenhouse Effect” with a consequent increase in night time temperature. In this study, we investigate the potential benefits of a range of thermic plastic films used as greenhouse cover materials on the vegetative and reproductive growth and development of Iceberg lettuce (Lactuca sativa L). Transplants were grown under thermic films and destructively harvested 4, 5, and 6 weeks after transplanting. Thermic films can increase night temperatures up to 2 ⁰C reducing the wide fluctuation in greenhouse temperature during winter compared to the standard commercial film and consequently increased the yield (leaf number, fresh weight, and dry weight) of lettuce plants. Lettuce plants grown under Clear film respond to cold stress by the accumulation of secondary products (phenolics, and flavonoids).

Keywords: Photoselective plastic films, thermic films, secondary metabolites.

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Authors: Nasim Abuali Galehdari, Thomas J. Ryan, Ajit D. Kelkar

Abstract:

In recent years, nanotechnology has played an important role in the design of an efficient radiation shielding polymeric composites. It is well known that, high loading of nanomaterials with radiation absorption properties can enhance the radiation attenuation efficiency of shielding structures. However, due to difficulties in dispersion of nanomaterials into polymer matrices, there has been a limitation in higher loading percentages of nanoparticles in the polymer matrix. Therefore, the objective of the present work is to provide a methodology to fabricate and then to characterize the functionally graded radiation shielding structures, which can provide an efficient radiation absorption property along with good structural integrity. Sandwich structures composed of Ultra High Molecular Weight Polyethylene (UHMWPE) fabric as face sheets and functionally graded epoxy nanocomposite as core material were fabricated. A method to fabricate a functionally graded core panel with controllable gradient dispersion of nanoparticles is discussed. In order to optimize the design of functionally graded sandwich composites and to analyze the stress distribution throughout the sandwich composite thickness, a finite element method was used. The sandwich panels were discretized using 3-Dimensional 8 nodded brick elements. Classical laminate analysis in conjunction with simplified micromechanics equations were used to obtain the properties of the face sheets. The presented finite element model would provide insight into deformation and damage mechanics of the functionally graded sandwich composites from the structural point of view.

Keywords: Nanotechnology, functionally graded material, radiation shielding, sandwich composites, finite element method.

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Authors: B. S. Raghavendra, D. Narayana Dutt

Abstract:

In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signal. The loglog plot of total number of boxes required to cover the curve versus size of the box used appears to be a straight line, whose slope is taken as an estimate of FD of the signal. The results are provided to demonstrate the performance of the proposed method using parametric fractal signals. The estimation accuracy of the method is compared with that of Katz, Sevcik, and Higuchi methods. In addition, some properties of the FD are discussed.

Keywords: Box-counting, Fractal dimension, Higuchi method, Katz method, Parametric fractal signals, Sevcik method.

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Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

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In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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Authors: S. J. Hosseini Ghoncheh, M. Paripour

Abstract:

In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Keywords: Benjamin-Bona-Mahony-Burgers equation, Cubic Bspline, Collocation method, Finite difference.

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Authors: Chen-Fu Wang, Lin-Ya Kung

Abstract:

For traditional painting materials, the artisan used to combine the pigments with different binders to create colors. As time goes by, the materials used for painting evolved from natural to chemical materials. The vast variety of ingredients used in chemical materials has complicated restoration work; it makes conservation work more difficult. Conservation work also becomes harder when the materials cannot be easily identified; therefore, it is essential that we take a more scientific approach to assist in conservation work. Paintings materials are high molecular weight polymer, and their analysis is very complicated as well other contamination such as smoke and dirt can also interfere with the analysis of the material. The current methods of composition analysis of painting materials include Fourier transform infrared spectroscopy (FT-IR), mass spectrometer, Raman spectroscopy, X-ray diffraction spectroscopy (XRD), each of which has its own limitation. In this study, FT-IR was used to analyze the components of the paint coating. We have taken the most commonly seen materials as samples and deteriorated it. The aged information was then used for the database to exam the temple painting materials. By observing the FT-IR changes over time, we can tell all of the painting materials will be deteriorated by the UV light, but only the speed of its degradation had some difference. From the deterioration experiment, the acrylic resin resists better than the others. After collecting the painting materials aging information on FT-IR, we performed some test on the paintings on the temples. It was found that most of the artisan used tune-oil for painting materials, and some other paintings used chemical materials. This method is now working successfully on identifying the painting materials. However, the method is destructive and high cost. In the future, we will work on the how to know the painting materials more efficiently.

Keywords: Temple painting, painting material, conservation, FT-IR.

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Authors: A. Evcin, N. Çiçek Bezir, R. Duman, N. Duman

Abstract:

Nowadays, a great concern is placed on the harmfulness of ultraviolet radiation (UVR) which attacks human bodies. Nanocarbon materials, such as carbon nanotubes (CNTs), carbon nanofibers (CNFs) and graphene, have been considered promising alternatives to shielding materials because of their excellent electrical conductivities, very high surface areas and low densities. In the present work, carbon nanofibers have been synthesized from solutions of Polyacrylonitrile (PAN)/ N,N-dimethylformamide (DMF) by electrospinning method. The carbon nanofibers have been stabilized by oxidation at 250 °C for 2 h in air and carbonized at 750 °C for 1 h in H2/N2. We present the fabrication and characterization of transparent and ultraviolet (UV) shielding CNF/polymer composites. The content of CNF filler has been varied from 0.2% to 0.6 % by weight. UV Spectroscopy has been performed to study the effect of composition on the transmittance of polymer composites.

Keywords: Electrospinning, carbon nanofiber, characterization, composites, nanofiber, ultraviolet radiation.

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Authors: Suman B. Chakraborty, Samir Banerjee

Abstract:

Stocking density is considered one of the important factors affecting fish growth. But, information related to impact of stocking density on growth performance of monosex tilapia population under the ecological conditions of Gangetic plains in West Bengal, India is limited. The aim of our study was to compare the growth potential of monosex tilapia at various stocking densities and to determine an ideal stocking density for culture of all-male monosex fish. The males were isolated by examination of genital papilla region and were stocked separately in 0.01 ha earthen ponds at different stocking densities (5000, 10000, 15000, 20000, 25000 and 30000 fingerlings/ha). It was found that the highest weight, length, daily weight gain, growth rate and protein content were observed for the 20000 fish/ha density class. Thus, culture of monosex tilapia at a density of 20000 fish/ha can be considered ideal for augmented production of the fish under Indian context.

Keywords: Growth potential, Nile tilapia, Pond culture, Stockingdensity.

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Erez Cohen

Abstract:

The study examines the socioeconomic impact of development of an advanced industry in Israel. The research method is based on data collected from the Israel Central Bureau of Statistics and from the National Insurance Institute (NII) databases, which provided information that allows to examine the Economic and Social Changes during the 1990s. The study examined the socioeconomic effects of the development of advanced industry in Israel. The research findings indicate that as a result of globalization processes, the weight of traditional industry began to diminish as a result of factory closures and the laying off of workers. These circumstances led to growing unemployment among the weaker groups in Israeli society, detracting from their income and thus increasing inequality among different socioeconomic groups in Israel and enhancement of social disparities.

Keywords: Globalization, Israeli advanced industry, public policy, socio-economic indicators.

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

Abstract:

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, Simulation

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Authors: Bachir Chemani, Halima Chemani

Abstract:

The objective of this study is to investigate the effect of adding coal to obtain insulating ceramic product. The preparation of mixtures is achieved with 04 types of different masse compositions, consisting of gray and yellow clay, and coal. Analyses are performed on local raw materials by adding coal as additive. The coal content varies from 5 to 20 % in weight by varying the size of coal particles ranging from 0.25mm to 1.60mm.

Initially, each natural moisture content of a raw material has been determined at the temperature of 105°C in a laboratory oven. The Influence of low-coal content on absorption, the apparent density, the contraction and the resistance during compression have been evaluated. The experimental results showed that the optimized composition could be obtained by adding 10% by weight of coal leading thus to insulating ceramic products with water absorption, a density and resistance to compression of 9.40 %, 1.88 g/cm³, 35.46 MPa, respectively. The results show that coal, when mixed with traditional raw materials, offers the conditions to be used as an additive in the production of lightweight ceramic products.

Keywords: Clay, coal, resistance to compression, insulating bricks.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

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 together 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: V. Ghadamyari, F. Samadi, F. Kowsary

Abstract:

An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: Shigeaki Sakurai, Youichi Kitahata, Ryohei Orihara

Abstract:

This paper proposes a method that discovers sequential patterns corresponding to user-s interests from sequential data. This method expresses the interests as constraint patterns. The constraint patterns can define relationships among attributes of the items composing the data. The method recursively decomposes the constraint patterns into constraint subpatterns. The method evaluates the constraint subpatterns in order to efficiently discover sequential patterns satisfying the constraint patterns. Also, this paper applies the method to the sequential data composed of stock price indexes and verifies its effectiveness through comparing it with a method without using the constraint patterns.

Keywords: Sequential pattern mining, Constraint pattern, Attribute constraint, Stock price indexes

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Authors: A. Sarıkaya, A. Akın

Abstract:

This study was carried out to investigate effects of Control (C), 18 bud/vine, 23 bud/vine, 28 bud/vine, 18 bud/vine + TKI-Humas (soil), 23 bud/vine + TKI-Humas (soil), 28 bud/vine + TKI-Humas (soil) applications on yield and yield components of Alphonse Lavallee grape cultivar. The results were obtained as the highest cluster weight (302.31 g) with 18 bud/vine application; the highest berry weight (6.31 g) with 23 bud/vine + TKI-Humas (soil) and (6.79 g) with 28 bud/vine + TKI-Humas (soil) applications; the highest maturity index (36.95) with 18 bud/vine + TKI-Humas (soil) application; the highest L* color intensity (33.99) with 18 bud/vine + TKI-Humas (soil); the highest a* color intensity (1.53) with 23 bud/vine + TKI-Humas (soil) application. The effects of applications on grape fresh yield, grape juice yield and b* color intensity values were not found statistically significant.

Keywords: Alphonse Lavallee grape cultivar, crop load, TKI-Humas substances (soil), yield, quality.

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Authors: T. Matsubayashi, T. Yamada

Abstract:

In this paper, we propose a fast and efficient method for drawing very large-scale graph data. The conventional force-directed method proposed by Fruchterman and Rheingold (FR method) is well-known. It defines repulsive forces between every pair of nodes and attractive forces between connected nodes on a edge and calculates corresponding potential energy. An optimal layout is obtained by iteratively updating node positions to minimize the potential energy. Here, the positions of the nodes are updated every global timestep at the same time. In the proposed method, each node has its own individual time and time step, and nodes are updated at different frequencies depending on the local situation. The proposed method is inspired by the hierarchical individual time step method used for the high accuracy calculations for dense particle fields such as star clusters in astrophysical dynamics. Experiments show that the proposed method outperforms the original FR method in both speed and accuracy. We implement the proposed method on the MDGRAPE-3 PCI-X special purpose parallel computer and realize a speed enhancement of several hundred times.

Keywords: visualization, graph drawing, Internet Map

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Authors: W. Handoko, F. Pahlevani, V. Sahajwalla

Abstract:

Dual-phase high carbon steels (DHCS) are commonly known for their improved strength, hardness, and abrasive resistance properties due to co-presence of retained austenite and martensite at the same time. Retained austenite is a meta-stable phase at room temperature, and stability of this phase governs the response of DHCS at different conditions. This research paper studies the effect of RA stability on corrosion behaviour of high carbon steels after they have been immersed into 1.0 M NaCl solution for various times. For this purpose, two different steels with different RA stabilities have been investigated. The surface morphology of the samples before and after corrosion attack was observed by secondary electron microscopy (SEM) and atomic force microscopy (AFM), along with the weight loss and Vickers hardness analysis. Microstructural investigations proved the preferential attack to retained austenite phase during corrosion. Hence, increase in the stability of retained austenite in dual-phase steels led to decreasing the weight loss rate.

Keywords: High carbon steel, austenite stability, atomic force microscopy, corrosion.

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Authors: Marzieh. Savoj, S. Amirhassan. Monadjemi

Abstract:

Iris localization is a very important approach in biometric identification systems. Identification process usually is implemented in three levels: iris localization, feature extraction, and pattern matching finally. Accuracy of iris localization as the first step affects all other levels and this shows the importance of iris localization in an iris based biometric system. In this paper, we consider Daugman iris localization method as a standard method, propose a new method in this field and then analyze and compare the results of them on a standard set of iris images. The proposed method is based on the detection of circular edge of iris, and improved by fuzzy circles and surface energy difference contexts. Implementation of this method is so easy and compared to the other methods, have a rather high accuracy and speed. Test results show that the accuracy of our proposed method is about Daugman method and computation speed of it is 10 times faster.

Keywords: Convolution, Edge detector filter, Fuzzy circle, Identification

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Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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