Numerical Solution of Generalized Burgers–Huxley Equation by Lie–Trotter Splitting Method

Çiçek, Yeşim; Korkut, Sıla Övgü

doi:10.1134/s1995423921010080

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…These methods include variational iteration method [34], variational iteration algorithm-I with an auxiliary parameter [3], the differential transform method [11], A fourth-order finite difference scheme [12], the discrete Adomian decomposition method [7], the residual power series [42], the finite difference method [23], non-polynomial cubic spline method [4], extended cubic B-spline approximation [6], finite-difference MacCormack method [17], C 1 Cubic quasi-interpolation splines [10], differential transform method and Padé approximant [43], double Laplace transform and double Laplace decomposition methods [31]. Many mathematicians have solved such problems to date, for more details, see [1,5,8,9,13,24,25,27,35]. Few authors have studied the spline method to solve partial differential equations, for instance, in [2,21,22,30,32,36,37,40].…”

Section: Introductionmentioning

confidence: 99%

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Mahmood¹,

Tahir²,

Jwamer³

2023

J. Math. Computer Sci.

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In this work, some types of nonlinear parabolic partial differential equations have been studied by means of the collocation method with cubic B-splines, without transformation or linearization. Here, the convergence analysis of the current scheme is also theoretically investigated. A few numerical examples are given to illustrate the viability and effectiveness of the proposed technique. The error norms l 2 and l ∞ are used to assess the accuracy of the current method. In this respect, the proposed method, keeping the real features of such problems, is able to save the behavior of nonlinear terms without facing any conventional drawbacks. Furthermore, it is mathematically shown and numerically seen that there is a good agreement between the approximation and the exact solutions. The current approach reduces the cost of calculation as well as the need for storage space at various parameters.

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Section: Introductionmentioning

confidence: 99%

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Mahmood¹,

Tahir²,

Jwamer³

2023

J. Math. Computer Sci.

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Numerical study of nonlinear generalized Burgers–Huxley equation by multiquadric quasi-interpolation and pseudospectral method

2022

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An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers’ equation

2021

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In the present paper, two effective numerical schemes depending on a second-order Strang splitting technique are presented to obtain approximate solutions of the one-dimensional Burgers' equation utilizing the collocation technique and approximating directly the solution by multiquadric-radial basis function (MQ-RBF) method. To show the performance of both schemes, we have considered two examples of Burgers' equation. The obtained numerical results are compared with the available exact values and also those of other published methods. Moreover, the computed L 2 and L ∞ error norms have been given. It is found that the presented schemes produce better results as compared to those obtained almost all the schemes present in the literature.

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Numerical Solution of Generalized Burgers–Huxley Equation by Lie–Trotter Splitting Method

Cited by 4 publications

References 18 publications

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Spline collocation methods for solving some types of nonlinear parabolic partial differential equations

Numerical study of nonlinear generalized Burgers–Huxley equation by multiquadric quasi-interpolation and pseudospectral method

An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers’ equation

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