Iterative solution of elliptic equations

IF 1.1 4区数学 Q1 MATHEMATICS

Electronic Journal of Qualitative Theory of Differential Equations Pub Date : 2022-01-01 DOI:10.14232/ejqtde.2022.1.34

P. Korman, D. Schmidt

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引用次数: 0

Abstract

We reduce solution of the Dirichlet problem ( x ∈ D ⊂ R m ) Δ u ( x ) + a ( x ) u ( x ) = f ( x ) in D , u = 0 on ∂ D to iterative solution of a simpler problem Δ u = f ( x ) in D , u = 0 on ∂ D , for which one can use either Fourier series or Green's function method. The method is suitable for numerical computations, particularly when one uses Newton's method for semilinear problems Δ u + g ( x , u ) = 0 in D , u = 0 on ∂ D , .

查看原文本刊更多论文

椭圆型方程的迭代解

我们将Dirichlet问题(x∈D∧R m) Δ u (x) + a (x) u (x) = f (x)在D中，u = 0在∂D中简化为一个更简单的问题Δ u = f (x)在D中，u = 0在∂D中，可以使用傅里叶级数或格林函数方法。该方法适用于数值计算，特别是当人们使用牛顿方法解决半线性问题Δ u + g (x, u) = 0在D中，u = 0在∂D中，。

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来源期刊

Electronic Journal of Qualitative Theory of Differential Equations 数学-数学

CiteScore

1.40

自引率

9.10%

发文量

审稿时长

3 months

期刊介绍： The Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE) is a completely open access journal dedicated to bringing you high quality papers on the qualitative theory of differential equations. Papers appearing in EJQTDE are available in PDF format that can be previewed, or downloaded to your computer. The EJQTDE is covered by the Mathematical Reviews, Zentralblatt and Scopus. It is also selected for coverage in Thomson Reuters products and custom information services, which means that its content is indexed in Science Citation Index, Current Contents and Journal Citation Reports. Our journal has an impact factor of 1.827, and the International Standard Serial Number HU ISSN 1417-3875. All topics related to the qualitative theory (stability, periodicity, boundedness, etc.) of differential equations (ODE''s, PDE''s, integral equations, functional differential equations, etc.) and their applications will be considered for publication. Research articles are refereed under the same standards as those used by any journal covered by the Mathematical Reviews or the Zentralblatt (blind peer review). Long papers and proceedings of conferences are accepted as monographs at the discretion of the editors.