A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers’ equation. (English) Zbl 1449.65300
Summary: In this paper, a high-order compact difference scheme is proposed for solving multidimensional nonlinear Burgers’ equation. The three-stage third-order total variation diminishing (TVD) Runge-Kutta scheme is employed in time, and the three-point combined compact difference (CCD) scheme is used for spatial discretization. The proposed TVD-CCD method is free of using Hopf-Cole transformation, and treats the nonlinear term explicitly. Thus it is very efficient and easy to implement. Our method is effective to capture shock wave, third-order accurate in time, and sixth-order accurate in space. In addition, we show the unique solvability of the CCD system under non-periodic boundary conditions. Numerical experiments are given to demonstrate the high efficiency and accuracy of the proposed method.
MSC:
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
total variation diminishing; sixth-order accuracy; combined compact difference; Burgers’ equation; high efficiencyReferences:
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