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| PARALLEL COMPUTING METHOD OF PURE ALTERNATIVE SEGMENT EXPLICIT-IMPLICIT DIFFERENCE SCHEME FOR NONLINEAR LELAND EQUATION |
| Ruifang Yan,Xiaozhong Yang,Shuzhen Sun |
| (Institute of Information and Computation, Mathematics and Physics School, North China Electric Power University, Beijing 102206, PR China) |
| DOI： |
| Abstract: |
| The research on the numerical solution of the nonlinear Leland equation has important theoretical significance and practical value. To solve nonlinear Leland equation, this paper offers a class of difference schemes with parallel nature which are pure alternative segment explicit-implicit (PASE-I) and implicit-explicit (PASI-E) schemes. It also gives the existence and uniqueness, the stability and the error estimate of numerical solutions for the parallel difference schemes. Theoretical analysis demonstrates that PASE-I and PASI-E schemes have obvious parallelism, unconditionally stability and second-order convergence in both space and time. The numerical experiments verify that the calculation accuracy of PASE-I and PASI-E schemes are better than that of the existing alternating segment Crank-Nicolson scheme, alternating segment explicit-implicit and implicit-explicit schemes. The speedup of PASE-I scheme is 9.89, compared to classical Crank-Nicolson scheme. Thus the schemes given by this paper are high efficient and practical for solving the nonlinear Leland equation. |
| Key words: nonlinear Leland equation; pure alternative segment explicit-implicit scheme (PASE-I); stability; truncation error analysis; parallel computing; numerical experiments |