高阶椭圆型偏微分方程奇异摄动问题一致收敛差分格式

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A Uniformly Convergent Difference Scheme for the Singular Perturbation Problem of a High Order Elliptic Differential Equation

摘要: 本文,我们讨论了一类高阶椭圆型偏微分方程奇异摄动问题。给出了连续问题解的先验估计。另外,我们还提供了一种数值求解该类问题的指数型差分格式。最后,证明了差分问题的解在能量范数意义下关于小参数一致收敛到连续问题的解。
- 椭圆型 /
- 奇异摄动 /
- 差分格式 /
- 一致收敛
Abstract: In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.
- elliptic /
- singular perturbation /
- difference scheme /
- uniform convergence

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