@Article{AAM-34-3,
author = {Yan, Ruifang and Yang, Xiaozhong and Sun, Shuzhen},
title = {Parallel Computing Method of Pure Alternative Segment Explicit-Implicit Difference Scheme for Nonlinear Leland Equation},
journal = {Annals of Applied Mathematics},
year = {2018},
volume = {34},
number = {3},
pages = {302--318},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {},
doi = {https://doi.org/2018-AAM-20579},
url = {https://global-sci.com/article/72723/parallel-computing-method-of-pure-alternative-segment-explicit-implicit-difference-scheme-for-nonlinear-leland-equation}
}