A class of conservative orthogonal spline collocation schemes for solving coupled Klein-Gordon-Schrodinger equations

作者：Wang Shanshan^*; Zhang Luming

来源：Applied Mathematics and Computation, 2008, 203(2): 799-812.

DOI：10.1016/j.amc.2008.05.089

• Klein-Gordon-Schrodinger equations
• orthogonal spline collocation scheme
• piecewise cubic hermite interpolation
• conservation law
• convergence
• solitary wave

A class of discrete-time orthogonal spline collocation schemes for solving coupled Klein-Gordon-Schrodinger equations with initial and boundary conditions are considered. These schemes are constructed by using piecewise cubic Hermite interpolations in space combined with finite difference methods in time. It is proved that the schemes have the conservation laws of discrete energy, and possess second order accuracy in maximum norm and fourth order in L(2)-norm for time and space, respectively. The conservation laws and rate of convergence are verified in numerical experiments. Moreover, the propagations of solitary waves and collisions of two head-on solitary waves are also well simulated.

• 出版日期2008-9-15
• 单位南京航空航天大学