双曲-双曲奇异摄动问题的指数型拟合差分格式
An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem
-
摘要: 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.Abstract: 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 weader compatibility 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.
-
[1] Su Yu-cheng and Lin Ping,Numerical solution of singular perturbation problem for hyperbolic differential equation with characteristic boundaries,Proceedings of the BAIL V Conference,Shanghai,Boole Press,Dublin 20-24 June(1988). [2] 苏煊城、林平.具有零阶退化方程的二阶双曲型方程奇异摄动问题的一致差分格式,应用学数和力学,11,4 (1990),283-294. [3] 苏爆城,林平,共有初始跳跃的双曲型万程奇异摄动问题的数值解,应用数学和力学,11,8(1990).665-676 [4] Geel,R.,Singular Perturbations of Hyperbolic Type,Mathematical Centre Tracts 98,Amsterdam(1978). [5] Bobisud,L.E.,The second initial-boundary value problem for a linear parabolic equation with a small parameter,Mich.Math.J.,15,4(1969),495-504. [6] Lees,M.,Energy inequalities for the solution of differential equations,Trans.Amer.Math.Soc.,94.1(1960). -
点击查看大图
计量
- 文章访问数: 2220
- HTML全文浏览量: 98
- PDF下载量: 504
- 被引次数: 0
下载:
