奇异摄动问题的一致收敛离散方法解的一致高阶精度外推

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基金项目: 国家自然科学基金资助项目

Uniformly Higher Order Accurate Extrapolations to Solution of Uniformly Convergent Discretization Methods for Singularly Perturbed Problems

摘要: 本文讨论基于整体误差一致展开式的一致收敛离散方法解的一致高阶精度外推.将该方法应用于非自共轭问题的Il'in-Allen-Southwell格式,我们得到了二阶一致收敛的外推解,并用数值计算说明该结论.

Abstract: We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.

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