双曲-双曲奇异摄动问题的指数型拟合差分格式

本文讨论带有关于x的一阶导数项的双曲奇异摄动初边值问题,在较弱的相容性条件下构造了问题的渐近解并证明了解的一致有效性.然后我们对原问题构造一个指数型拟合差分格式并建立了离散能量不等式.最后我们证明差分问题的解一致收敛于原问题的精确解.

An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem

In this paper we discuss an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weaker compativility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem.