A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is con...Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.展开更多
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 w...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.展开更多
针对时间分数阶慢扩散方程,提出一类并行差分方法——交替分段纯显-隐(pure alternative segment explicit-implicit,PASE-I)和交替分段纯隐-显(pure alternative segment implicit-explicit,PASI-E)差分方法。这类方法是将古典显式格...针对时间分数阶慢扩散方程,提出一类并行差分方法——交替分段纯显-隐(pure alternative segment explicit-implicit,PASE-I)和交替分段纯隐-显(pure alternative segment implicit-explicit,PASI-E)差分方法。这类方法是将古典显式格式、古典隐式格式与交替分段技术相结合构造出的一类具有并行本性的差分方法。理论证明了PASE-I和PASI-E格式解的存在唯一性,采用傅里叶方法和数学归纳法证明了格式是无条件稳定且收敛的。数值试验表明:PASE-I格式和PASI-E格式具有明显的并行计算性质,为空间二阶、时间2-α阶收敛,并且在计算效率上相比串行的隐式格式有大幅度提高,本方法求解时间分数阶慢扩散方程是可行的。展开更多
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
文摘Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.
基金supported by National Natural Science Foundation of China(No.11371135)the Fundamental Research Funds for the Central Universities(WK2014ZZD10)
文摘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.
文摘针对时间分数阶慢扩散方程,提出一类并行差分方法——交替分段纯显-隐(pure alternative segment explicit-implicit,PASE-I)和交替分段纯隐-显(pure alternative segment implicit-explicit,PASI-E)差分方法。这类方法是将古典显式格式、古典隐式格式与交替分段技术相结合构造出的一类具有并行本性的差分方法。理论证明了PASE-I和PASI-E格式解的存在唯一性,采用傅里叶方法和数学归纳法证明了格式是无条件稳定且收敛的。数值试验表明:PASE-I格式和PASI-E格式具有明显的并行计算性质,为空间二阶、时间2-α阶收敛,并且在计算效率上相比串行的隐式格式有大幅度提高,本方法求解时间分数阶慢扩散方程是可行的。
