A class of conservative orthogonal spline collocation schemes for solving coupled Klein–Gordon–Schrödinger equations

A class of discrete-time orthogonal spline collocation schemes for solving coupled Klein–Gordon–Schrödinger 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 L2L2-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.