【摘要】 为研究适合在并行计算机上高效率解一类非线性发展方程的计算方法,给出了一类非线性发展方程,并对其应用古典显格式、古典隐格式以及Saul′yev型非对称差分格式,构造了求解这一类非线性发展方程的交替分组显示AGE-3方法.并且证明了该方法的无条件稳定性以及具有并行性兼顾的结果.数值实验说明该方法具有良好的并行性、有效性,且误差小、精度高,宜于直接在并行计算机上使用.更多还原

【Abstract】 In order to study computational methods for effectively solving a class of nonlinear evolution equations on parallel computers, a class of nonlinear evolution equations is first given. By employing the classical explicit scheme, the classical implicit scheme and Saul′yev asymmetries difference scheme, the AGE\|3 method for a class of nonlinear evolution equations is constructed. And this method′s unconditional stability and parallelity are proved. Numerical experiment shows that this method is of good parallelism, effectiveness, high accuracy, and is suitable to be directly used on parallel computers.更多还原