A numerical scheme for the generalized Burgers–Huxley equation

Singh, Brajesh Kumar; Arora, Geeta; Singh, Manoj Kumar

doi:10.1016/j.joems.2015.11.003

Cited by 43 publications

(28 citation statements)

References 39 publications

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“…Mittal and Jain [54] obtained a numerical solution of nonlinear Burgers equation using a modified cubic B-spline collocation method. Singh et al [55] developed a numerical scheme for solving the GBH equation using modified cubic B-spline differential quadrature method (MCB-DQM) and numerical results can be obtained using SSP-RK43 scheme. Reza [56] implemented the cubic B-spline collocation scheme based on the finite difference scheme for solving the GBH equation.…”

Section: Model IImentioning

confidence: 99%

“…Table 2 shows a comparison of the absolute errors at = 3.9, = 1, 2, 3 obtained by proposed method HBSCM with the methods existing in the literature named compact finite difference scheme (CFDS) [26], a fourth-order improved numerical scheme (FONS) [33], variational iteration method (VIM) [36], Adomian decomposition method (ADM) [38,40], implicit exponential finite difference method (IEFM) [42], and modified cubic B-spline (MCBS) [55]. The obtained results are compared with Haar wavelet method (HWM) [46] at = 0.8 in Table 3 while a comparison between HBSCM and a new domain decomposition method (NDDA) [22] can be observed in Table 4.…”

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

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Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

Wasim

Abbas

Noor‐ul‐Amin

2018

Mathematical Problems in Engineering

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In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier) method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.

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Section: Model IImentioning

confidence: 99%

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

Wasim

Abbas

Noor‐ul‐Amin

2018

Mathematical Problems in Engineering

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“…In this paper, the combination of the trigonometric cubic B-spline(TCB) collocation method and Crank-Nicolson schme(CNS) is applied to integrate FE into a system of nonlinear equations. Some methods endowed with splines are set up to solve the differential equations [17,20,22,23]. There exist spline based numerical methods for the FE in the literature: The FE is solved numerically by setting up an Galerkin method with cubic B-spline over the finite elements in work [2].…”

Section: Introductionmentioning

confidence: 99%

The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method

Hepson¹,

Dağ²

2017

Communications in Numerical Analysis

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In this study, we set up a numerical technique to get approximate solutions of Fisher's equation which is integrated fully with help of combination of the trigonometric cubic B-spline functions in space and Crank-Nicolson in time. Numerical results have been presented to show utility of the current algorithm by studying three test problems. Solutions of the fisher equation are shown to model the wave front numerically and interaction of diffusion and reaction is observed for the Fisher eqaution.

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“…Schemes such as the adomian decomposition [14], homotopy perturbation [15], homotopy analysis [16], and reduced differential transform [17] were proposed to solve the initial value problem of the Burgers-Huxley equation. Moreover, some authors considered the initial boundary value problem of this equation and used spectral collocation [18], finite-difference [19,20], Haar wavelet [21] and modified cubic B-spline differential quadrature [22] methods for its solution.…”

Section: Introductionmentioning

confidence: 99%

Highly Accurate Scheme for the Cauchy Problem of the Generalized Burgers-Huxley Equation

2016

APH

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In this paper, a weighted algorithm, based on the reduced differential transform method, is introduced. The new approach is adopted in the approximate analytical solution of the Cauchy problem for the Burgers-Huxley equation. The proposed scheme considers the initial and boundary conditions simultaneously for obtaining a solution of the equation. Several examples are discussed demonstrating the performance of the algorithm.

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A numerical scheme for the generalized Burgers–Huxley equation

Cited by 43 publications

References 39 publications

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

The Numerical Approach to the Fisher's Equation via Trigonometric Cubic B-spline Collocation Method

Highly Accurate Scheme for the Cauchy Problem of the Generalized Burgers-Huxley Equation

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