A sixth-order compact finite difference scheme to the numerical solutions of Burgers’ equation

Sarı, Murat; Gürarslan, Gürhan

doi:10.1016/j.amc.2008.12.012

Cited by 57 publications

(42 citation statements)

References 34 publications

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“…Another sixth-order compact finite difference method has been used in [77]. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time have been combined.…”

Section: Survey Of Different Techniquesmentioning

confidence: 99%

Contemporary review of techniques for the solution of nonlinear Burgers equation

Dhawan

Kapoor

Kumar

et al. 2012

Journal of Computational Science

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Section: Survey Of Different Techniquesmentioning

confidence: 99%

Contemporary review of techniques for the solution of nonlinear Burgers equation

Dhawan

Kapoor

Kumar

et al. 2012

Journal of Computational Science

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“…The exact solution is given by u(x, t) = 2π 1 Re Σ ∞ n=1 a n exp(−n 2 π 2 1 Re t)n sin(nπx) a 0 + Σ ∞ n=1 a n exp(−n 2 π 2 1 Re t)n cos(nπx) and the Fourier coefficients a 0 = In this problem, we set v = 1, ∆t = 0.00001, ∆x = 0.0125 for all numerical methods. Table 1 lists our results and results obtained by researchers [42][43][44] using the Hopf-Cole(HC), Restrictive Hopf-Cole(RHC), Restrictive Padé Approximation (RPA) and TVD-CFD (TVCF) methods. It is shown that the CCD-TVD method offers better results than other existing schemes.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers’ equation

Pan

Yue

et al. 2020

Comp. Appl. Math.

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In this paper, an efficient and high-order accuracy finite difference method is proposed for solving multidimensional nonlinear Burgers' equation. The third-order three stage Runge-Kutta total variation diminishing (TVD) scheme is employed for the time discretization, and the three-point combined compact difference (CCD) scheme is used for spatial discretization. Our method is third-order accurate in time and sixth-order accurate in space. The CCD-TVD method treats the nonlinear term explicitly thus it is very efficient and easy to implement. In addition, we prove the unique solvability of the CCD system under non-periodic boundary conditions. Numerical experiments including both two-dimensional and three-dimensional problems have been conducted to demonstrate the high efficiency and accuracy of the proposed method.

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“…In addition, various versions of the FD schemes have been analyzed and implemented successfully by some researchers [13][14][15][16][17][18][19][20][21] for their own problems. In this work, to compute the solutions HIGH-ORDER FINITE DIFFERENCE 1297 of the present problem, up to tenth-order FD scheme in space and a fourth-order Runge-Kutta (RK4) scheme in time were implemented for computing solutions of the generalized BurgersFisher equation.…”

Section: Introductionmentioning

confidence: 99%

High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation

Sarı

Gürarslan

Zeytinoğlu

2009

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYUp to tenth-order finite difference (FD) schemes are proposed in this paper to solve the generalized Burgers-Fisher equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order FD schemes in space and fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the present methods. The produced results are also seen to be more accurate than some available results given in the literature. Comparisons showed that there is very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present methods are seen to be very good alternatives to some existing techniques for such realistic problems.

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A sixth-order compact finite difference scheme to the numerical solutions of Burgers’ equation

Cited by 57 publications

References 34 publications

Contemporary review of techniques for the solution of nonlinear Burgers equation

Contemporary review of techniques for the solution of nonlinear Burgers equation

A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers’ equation

High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation

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