解色散方程的加耗散项半显式与显式差分格式

Introducing Dissipative Term into Semi-Explicit and Explicit Difference Schemes for Solving Dispersion Equation

解色散方程U_t=aU_(■■■)的大多数常见的显式差分格式,例如文[1]中的差分格式,其稳定性条件是苛刻的.这一困难可由在常规的显式差分格式中引入耗散项而得到克服.基于此.我们导出一类新的无条件稳定的两层的半显式差分格式及若干具有高稳定性的三层显式格式,它们包含了若干已知的具有高稳定性的三层显式格式.

The stability condition of most conventional explicit schemes, e. g. the schemes in reference [1], for solving the dispersion equation U_1=AU_(xxx) is harsh. This is a difficulty which can be overcome by introducing a dissipative term into conventional explicit schemes. On this basis, the author derives a class of two-level new semi-explicit schemes with unconditional stability and also a number of threelevel explicit schemes with high stability of which some are already known.