发展方程谱方法的显隐Runge-Kutta方法  

Implicit-explicit Runge-Kutta method for solving evolution equations with spectral method

作　　者：白景阁 马和平[1] BAI Jingge;MA Heping(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2018年第3期651-664,共14页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11571224)

摘　　要：针对非齐次两点边值问题,首先给出了结合谱方法解发展方程的显式四阶RungeKutta方法的有效实现形式,又通过待定系数法构造出显隐Runge-Kutta的三阶格式,证明其为L-稳定.随后给出显隐Runge-Kutta高阶方法的有效实现形式,用此格式计算了Burgers方程和Korteweg-de Vries (KdV)方程,并将计算结果与目前常用的时间离散方法进行了比较.数值结果表明这些方法的有效性及可行性.The nonhomogeneous two-point boundary value problem is considered in this paper.Firstly,the effective implementation of the fourth-order explicit Runge-Kutta method combining the spectral method is given.Then,a third-order explicit-implicit Runge-Kutta scheme is constructed by the method of undeter-mined coefficients.It is proved to be L-stable.The effective implementation is given too.The Burgers equation and the Korteweg-de Vries(KdV)equation are computed using these schemes.Numerical results indicate that our method is efficient and easy to be implemented.

关 键 词：非齐次 BURGERS方程 显隐Runge-Kutta 有效实现 

分 类 号：O175.14[理学—数学]