Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

Bukhari, Mutia; Arshad, Muhammad Nadeem; Batool, Safeera; Saqlain, Syed Muhammad

doi:10.21833/ijaas.2017.05.001

Cited by 9 publications

(10 citation statements)

References 29 publications

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“…Reza [57] developed a numerical method based on exponential B-spline with finite difference approximations to solve the GBF equation. Recently, Bukhari et al [58] applied local radial basis functions differential collocation (LRBDQ) method to compute the numerical solution of GBH equation.…”

Section: Model IImentioning

confidence: 99%

“…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. The results of the proposed method in terms of errors comparative to Local Radial Basis Function Differential Collocation method (LRBFDQ) [58] is provided in Table 5. It can be observed that increase in Δ did not disturb the accuracy of HBSCM and our method still approximates the exact solution quite adequately due to hybrid parameter.…”

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

“…It is pertinent to claim that the proposed method provides accurate and improves results as compared to others. (2) When = 0.001, = 0.001, = 0.001, Δ = 0.0001, = 1, = 2, GBH equation can be [58] described as follows:…”

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

“…In Table 6, the error norms are calculated at different time levels for Δ = 0.0001 and compared with LRBFDQ [58]. A comparison of the absolute errors calculated by HBSCM at = 1, 2, 8 is presented in Table 7 with the existing methods named spectral collocation method (SCM) [20] and IEFM [42].…”

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

See 3 more Smart Citations

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%

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

Section: Numerical Test Cases For Model Imentioning

confidence: 99%

See 2 more Smart Citations

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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show abstract

“…In general it is difficult and sometimes impossible to get exact solution of such type of nonlinear PDEs. Researchers employed different numerical techniques which include discrete Adomian decomposition method [12], Haar wavelet method [13], Adomian decomposition method [14], meshless collocation method based on RBF [15] and local meshless method [16] for the solution of Burgers' Huxley equation. The Huxley model equation [17] describes nerve pulse propagation in nerve fibres and wall motion in liquid crystals [18].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Local Formulation for Time–Dependent PDEs

et al. 2019

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In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.

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A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics

Usman

Hamid

Khalid

et al. 2020

Numerical Methods Partial

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In this paper, we present a novel approach based on shifted Gegenbauer wavelets to attain approximate solutions of some classed of time-fractional nonlinear problems. First, we present the approximation of a function of two variables u(x,t) with help of shifted Gegenbauer wavelets and then some novel operational matrices are proposed with the help of piecewise functions to investigate the positive integer derivative (D x and D t), fractional-order derivative (P x and P t), fractional-order integration (J x and J t) and delay terms (D a b How to cite this article: Usman M, Hamid M, Khalid MSU, Haq RU, Liu M. A robust scheme based on novel-operational matrices for some classes of time-fractional nonlinear problems arising in mechanics and mathematical physics.

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Numerical solution of generalized Burger’s-Huxley equation using local radial basis functions

Cited by 9 publications

References 29 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

An Efficient Local Formulation for Time–Dependent PDEs

A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics

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