Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-04-12 DOI:10.1016/j.aml.2025.109571

Maryam Mohammadi , Alvise Sommariva , Marco Vianello

引用次数: 0

Abstract

We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving almost sure nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed boundary conditions. We also show some numerical tests, where the fictitious centers are local random perturbations of predetermined collocation points.

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带随机虚拟中心的多谐样条椭圆方程Kansa配置的不均匀性

我们进一步研究了非对称Kansa配置的不一致开问题，证明了具有多谐样条和随机虚中心的二阶椭圆方程的Kansa矩阵在混合边界条件下的几乎肯定非奇异性。我们还给出了一些数值测试，其中虚拟中心是预定配点的局部随机扰动。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.