A Difference Method With Intrinsic Parallelism For The Variable-Coefficient Compound Kdv-Burgers Equation

In this paper, the difference method with intrinsic parallelism is studied in order to meet the needs of quickly solving the variable-coefficient compound KdV-Burgers equation. The classical Crank-Nicolson (C-N) scheme is segmented on the basis of the alternating segment difference technique. And four different types of Saul'yev asymmetric schemes are alternately used at the segment points. Then we obtain the alternating segment Crank-Nicolson (ASC-N) difference scheme for the variable-coefficient compound KdV-Burgers equation. Theoretical analyses prove the existence and uniqueness of solution to ASC-N scheme, the linear absolute stability and the second-order convergence in time and space. Numerical experiments show that when the computational accuracy of the ASC-N scheme is similar to that of the C-N scheme, the computational efficiency of the ASC-N scheme is significantly higher than that of the C-N scheme. It shows that the difference method with intrinsic parallelism in this paper can effectively solve the variable-coefficient compound KdV-Burgers equation. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.