Radial basis functions method for numerical solution of the modified equal width equation

Dereli, Yılmaz

doi:10.1080/00207160802395908

Cited by 12 publications

(18 citation statements)

References 15 publications

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“…It is clear to say that the present results are superior of the given values. The present invariants are almost constant. Application It is needed to narrow the solution domain to [0, 70] to compare the present results with those in [9, 19, 20]. The same parameters and time increment Δ t = 0.05 are used and the numerical results are reported in Table 5.…”

Section: Applications and Resultsmentioning

confidence: 99%

“…Three invariants are almost constant. [19][20][21] are given in Table 8. The present results are better than earlier works except the L 2 error value of the third variant of the quintic B-spline collocation method (QBCM3) [21].…”

Section: Behavior Of the Single Solitary Wavementioning

confidence: 99%

“…The present invariants are almost constant. For the comparison with other works[19][20][21] it is needed to narrow the solution domain to the [0, 70]. Comparison of the present results with other applications…”

mentioning

confidence: 91%

“…Because of the importance of the MEW equation in nonlinear media, many researchers have tried to obtain the numerical solutions of the equation. For example, Evans and Raslan used collocation method [8], Esen used lumped Galerkin method [9], Çelikkaya used operator splitting method [10], Esen and Kutluay used finite difference method [11], Essa used multigrid method [12], Karakoç et al used collocation method based on different linearization techniques [13], Geyikli and Karakoç used subdomain method [14], Karakoç and Geyikli used sextic B-spline based subdomain method [15], Geyikli and Karakoç used Petrov-Galerkin method [16], Karakoç and Geyikli used lumped Galerkin method [17], Raslan et al used finite difference method [18], Dereli used collocation method via radial basis functions [19], Zaki used Petrov-Galerkin method [20], Saka used collocation method based on quintic B-splines [21].…”

Section: Introductionmentioning

confidence: 99%

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Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

Başhan

Yağmurlu

Uçar

et al. 2020

Numerical Methods Partial

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The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B-spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.

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Section: Applications and Resultsmentioning

confidence: 99%

Section: Behavior Of the Single Solitary Wavementioning

confidence: 99%

mentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

Başhan

Yağmurlu

Uçar

et al. 2020

Numerical Methods Partial

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“…By discretizing this trial space, the original problem is transformed to the problem of finding unknown coefficients (the coefficients may be the solution values as in the meshless local Petrov-Galerkin (MLPG) approach). The moving least squares approximations and RBFs are the most popular approaches in the literatures for trial approximations; see, for example, [1][2][3][4][5][6][7][8][9].To find the unknown coefficients, the approximate solution should be tested to satisfy the governing equations and boundary conditions. The method proposed in this paper uses the multiquadric (MQ) RBFs for trial approximation and the local weak approach for testing.…”

Section: Introductionmentioning

confidence: 99%

Solving 2D Reaction-Diffusion Equations with Nonlocal Boundary Conditions by the RBF-MLPG Method

Shirzadi

2014

Comput Math Model

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This paper is concerned with the development of a new approach for the numerical solution of linear and nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal boundary conditions. Proper finite-difference approximations are utilized to discretize the time variable. Then, the weak equations of resultant elliptic type PDEs are constructed on local subdomains. These local weak equations are discretized by using the multiquadric (MQ) radial basis function (RBF) approximation where an iterative procedure is proposed to treat the nonlinear terms in each time step. Numerical test problems are given to verify the accuracy of the obtained numerical approximations and stability of the proposed method versus the parameters of the nonlocal boundary conditions.

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A new perspective for the numerical solution of the Modified Equal Width wave equation

Başhan

Yağmurlu

Uçar

et al. 2021

Math Methods in App Sciences

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Finding the approximate solutions to natural systems in the branch of mathematical modelling has become increasingly important and for this end various methods have been proposed. The purpose of the present paper is to obtain and analyze the numerical solutions of Modified Equal Width equation (MEW). This equation is one of those equations used to model nonlinear phenomena which has a significant role in several branches of science such as plasma physics, fluid mechanics, optics and kinetics. Firstly, for the discretization of spatial derivatives, a fifth‐order quintic B‐spline based scheme is directly implemented. Secondly, a forward finite difference formula is applied for the temporal discretization of derivatives with respect to time. Simulation results establish the validity and applicability of the suggested technique for a wide range of nonlinear equations. Then, the newly obtained theoretical consequences are numerically justified by the simulations and test problems. These illustrative test problems are presented verifying the superiority of the newly presented scheme compared to other existing schemes and techniques. The suggested method with symbolic computational software such as, Matlab, is proven as an effective way to obtain the soliton solutions of several nonlinear partial differential equations (PDEs). Finally, the newly obtained results are presented graphically to justify the approximate findings.

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Radial basis functions method for numerical solution of the modified equal width equation

Cited by 12 publications

References 15 publications

Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

Solving 2D Reaction-Diffusion Equations with Nonlocal Boundary Conditions by the RBF-MLPG Method

A new perspective for the numerical solution of the Modified Equal Width wave equation

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