拟线性双曲—抛物奇异摄动问题的变步长差分格式

Asymptotic Expansion for Quasi-liner Singular Perturbation Problem of Hyperbolic—Parrabolic Partial Differential Equations

根据关于小参数ε一致收敛的要求,构造了t方向的变步长网格函数,建立了时间方向上的非均匀网格,然后在此非均匀网格上构造了关于小参数收敛的七点三层隐式差分格式,证明了该差分格式关于ε的一致收敛性.

The mesh function is first constructed with variable step lengths along the direction of time under the condition that the perturbation function is uniformly convergent with respect to the small parameter ε. Then a non-uniform mesh is constructed along the direction of time. The uniformly convergence of this difference scheme with respect to the small parameter is finally proved.