Numerical solutions of Burgers–Huxley equation by exact finite difference and NSFD schemes

Zibaei, Sadegh; Zeinadini, M.; Namjoo, Mehran

doi:10.1080/10236198.2016.1173687

Cited by 24 publications

(10 citation statements)

References 24 publications

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“…An exact finite difference scheme is a finite difference model for which the solution to the difference equation has the same general solution as the associated differential equation [38]. Recently, there has been an increasing interest in exact finite difference models for particular ODEs and PDEs, because they let a better construction of finite difference schemes (see [39,40] and the references therein). These finite difference models do not exhibit numerical instabilities.…”

Section: Exact Finite Difference Schemes For Kdvb(2 1 2) Equationmentioning

confidence: 99%

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Köroğlu

2020

Adv Differ Equ

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We consider the generalized KdV-Burgers KdVB(p, m, q) equation. We have designed exact and consistent nonstandard finite difference schemes (NSFD) for the numerical solution of the KdVB(2, 1, 2) equation. In particular, we have proposed three explicit and three fully implicit exact finite difference schemes. The proposed NSFD scheme is linearly implicit. The chosen numerical experiment consists of tanh function. The NSFD scheme is compared with a standard finite difference(SFD) scheme. Numerical results show that the NSFD scheme is accurate and efficient in the numerical simulation of the kink-wave solution of the KdVB(2, 1, 2) equation. We see that while the SFD scheme yields numerical instability for large step sizes, the NSFD scheme provides reliable results for long time integration. Local truncation error reveals that the NSFD scheme is consistent with the KdVB(2, 1, 2) equation.

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Section: Exact Finite Difference Schemes For Kdvb(2 1 2) Equationmentioning

confidence: 99%

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Köroğlu

2020

Adv Differ Equ

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“…These schemes were proposed by Mickens,() and successively, their use has been investigated in several fields. () NSFD schemes are mainly constructed based upon the following basic rules. (i)The orders of discrete derivatives should be equal to the orders of corresponding derivatives appearing in the differential equations. Discrete representations for derivatives, in general, have nontrivial denominator functions.For example, in the classical sense, the first derivative approximation can be represented as

u_{t} ≅ \frac{u_{j}^{n + 1} - u_{j}^{n}}{Δ t}, u_{x} ≅ \frac{u_{j + 1}^{n} - u_{j}^{n}}{Δ x},

where

u_{j}^{n}

is an approximation to u ( x j , t n ).…”

Section: Nonstandard Finite‐difference Schemesmentioning

confidence: 99%

“…These schemes were proposed by Mickens, 13,20 and successively, their use has been investigated in several fields. [15][16][17][18][19][21][22][23][24][25][26] NSFD schemes are mainly constructed based upon the following basic rules.…”

Section: Nonstandard Finite-difference Schemesmentioning

confidence: 99%

Nonstandard finite‐difference scheme to approximate the generalized Burgers‐Fisher equation

Namjoo

Zeinadini

Zibaei

2018

Math Methods in App Sciences

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In this paper, numerical solution of the generalized Burgers‐Fisher (BF) equation is presented on the basis of the nonstandard finite‐difference (NSFD) scheme. At first, two exact finite‐difference schemes for the BF equation are obtained. Afterwards, an NSFD scheme is presented for this equation. The positivity, consistency, and boundedness of the scheme are discussed. The numerical results obtained by the NSFD scheme is compared with the exact solution and some available methods to verify the accuracy and efficiency of the NSFD scheme.

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“…There are a lot of results of EDS for both ordinay and partial differential equations such as [7,12,13,[22][23][24]26]. Among them EDS for linear differential equations or system of differential equations with constant coefficients have attracted a special interest [12,16,17,24].…”

Section: Introductionmentioning

confidence: 99%

Exact Finite Difference Schemes for Three-Dimensional Linear Systems with Constant Coefficients

Tuan

2017

Vietnam J. Math.

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In this paper implicit and explicit exact difference schemes (EDS) for system x ′ = Ax of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for problems with periodic solutions on very large time interval demonstrate the efficiency and exactness of the EDS compared with high-order numerical methods. This result can be extended for constructing EDS for general systems of n linear differential equations with constant coefficients and nonstandard finite difference (NSFD) schemes preserving stability properties for quasi-linear system of equations x ′ = Ax + f (x).

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Numerical solutions of Burgers–Huxley equation by exact finite difference and NSFD schemes

Cited by 24 publications

References 24 publications

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Exact and nonstandard finite difference schemes for the generalized KdV–Burgers equation

Nonstandard finite‐difference scheme to approximate the generalized Burgers‐Fisher equation

Exact Finite Difference Schemes for Three-Dimensional Linear Systems with Constant Coefficients

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