Two Eight-point Difference Schemes Of The Dispersive Equation

The initial-boundary value problem of dispersive equation is a kind of mathematical model, which is extracted by physical phenomenon of solitary waves. Researching its difference schemes have attracted people' much attentions. Because most of the difference solutions of non-linear partial differential equation is generalization and application of solving liner partial differential ones,a series of schemes have appeared on difference solutions of linear dispersive equation recent years and solving its difference schemes have the significance of mathematics theory and practical application. The explicit schemes of three-order dispersive equation have simple structures and calculations but strict limitation while the implicit schemes have absolute conditions but can not parallel compute directly and have a large amount of calculation. In this paper, I have followed the way of other scholars and created new methods and got two eight-point difference schemes. I have calculated and contracted their truncation errors and analysed their stability analysis by using multi-dimensional Taylor equation and discrete Fourier transform.At last, based on the difference schemes,the Matlab program is obtained by the algorithm. According to the calculational results and comparing with their precision,stability and practicality,this paper can provide offer to higher order and more complicated partial differential equations' schemes.