New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

PAN Yueyue; YANG Xiaozhong

doi:10.21656/1000-0887.430128

Volume 44 Issue 5

May 2023

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PAN Yueyue, YANG Xiaozhong. New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation[J]. Applied Mathematics and Mechanics, 2023, 44(5): 583-594. doi: 10.21656/1000-0887.430128

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New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

doi: 10.21656/1000-0887.430128

PAN Yueyue^1
,,
YANG Xiaozhong^{2
,
,}

1.
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, P.R.China
2.
Institute of Information and Computing, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R.China

Received Date: 2022-04-11
Rev Recd Date: 2022-06-14
Publish Date: 2023-05-01

Abstract

Abstract

The KdV-Burgers equation as a standard equation for turbulent, has a profound physical background and its fast numerical methods are of great practical application value. A new class of parallel difference schemes were proposed for the KdV-Burgers equation. Based on the alternating segment technology, the mixed alternating segment Crank-Nicolson (MASC-N) difference scheme was constructed with the classic Crank-Nicolson (C-N) scheme, the explicit and implicit schemes. The theoretical analyses indicate that, the MASC-N scheme is uniquely solvable, linearly absolutely stable and 2nd-order convergent. Numerical experiments show that, the MASC-N scheme has higher precision and efficiency than the C-N scheme. Compared with the ASE-I and ASC-N difference schemes, the MASC-N parallel difference scheme has the best performance, and can effectively solve the KdV-Burgers equation.
- KdV-Burgers equation,
- MASC-N parallel difference scheme,
- linear absolute stability,
- convergence,
- numerical experiment

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References(27)

References

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