求解泊松方程近似特解的局部赫米特法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-01-21 DOI:10.1016/j.aml.2025.109471

Kwesi Acheampong, Huiqing Zhu

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引用次数: 0

摘要

本文提出了求解泊松方程的近似特解的局部Hermite法。与局部近似特解方法（LMAPS）不同，该方法仅利用径向基函数的特解逼近配置节点不同局部邻域解的函数值，而采用混合基函数，结合局部模板内的径向基函数及其拉普拉斯算子的特解，同时逼近解及其拉普拉斯算子。数值实验表明，该方法显著提高了LMAPS的精度。

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Localized Hermite method of approximate particular solutions for solving the Poisson equation

In this paper, we propose a localized Hermite method of approximate particular solutions (LHMAPS) for solving the Poisson equation. Unlike the localized method of approximate particular solutions (LMAPS) that approximates only function values of the solution in different local neighborhoods of collocation nodes by using particular solutions of radial basis functions, the proposed method employs mixed basis functions, combining radial basis functions and their particular solutions for the Laplace operator within local stencils to simultaneously approximate both the solution and its Laplacian. Numerical experiments show that significantly improves the accuracy of LMAPS.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.