Parallel Computing Method of Pure Alternative Segment Explicit-Implicit Difference Scheme for Nonlinear Leland Equation
Year: 2018
Author: Ruifang Yan, Xiaozhong Yang, Shuzhen Sun
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 3 : pp. 302–318
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 highly efficient and practical for solving the nonlinear Leland equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-AAM-20579
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 3 : pp. 302–318
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: nonlinear Leland equation pure alternative segment explicit-implicit scheme (PASE-I) stability truncation error analysis parallel computing numerical experiments.