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一种用于求解三维椭圆型和双曲型偏微分方程的边值方法。

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

作者信息

Biala T A, Jator S N

机构信息

Department of Mathematics and Computer Science, Jigawa State University, Kafin Hausa, P.M.B 048, Kafin Hausa, Nigeria.

Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044 USA.

出版信息

Springerplus. 2015 Oct 9;4:588. doi: 10.1186/s40064-015-1348-1. eCollection 2015.

DOI:10.1186/s40064-015-1348-1
PMID:26543723
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4627984/
Abstract

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

摘要

在本文中，应用边界值方法求解三维椭圆型和双曲型偏微分方程。对两个空间变量（y，z）的偏导数使用有限差分近似进行离散化，以得到关于第三个空间变量（x）的常微分方程（ODE）的大型系统。利用插值和配置技术，开发了一种连续格式，并用于获得离散方法，这些离散方法通过块统一方法应用于求解所得的大型ODE系统以获得近似解。研究了几个测试问题以阐明求解过程。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/d47d24c47958/40064_2015_1348_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/62e4910a8bec/40064_2015_1348_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/e19b2b247c63/40064_2015_1348_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/40675218f192/40064_2015_1348_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/2023bce7a09a/40064_2015_1348_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/d47d24c47958/40064_2015_1348_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/62e4910a8bec/40064_2015_1348_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/e19b2b247c63/40064_2015_1348_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/40675218f192/40064_2015_1348_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/2023bce7a09a/40064_2015_1348_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/8694/4627984/d47d24c47958/40064_2015_1348_Fig5_HTML.jpg

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本文引用的文献

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Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.通过指数函数和Exp(-ϕ(ξ))-展开法研究Vakhnenko-Parkes方程的孤立波解
Springerplus. 2014 Nov 25;3:692. doi: 10.1186/2193-1801-3-692. eCollection 2014.
2
New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.求解非线性演化方程的新型扩展(G'/G)-展开法：(3 + 1)维势-YTSF方程
Springerplus. 2014 Mar 5;3:122. doi: 10.1186/2193-1801-3-122. eCollection 2014.
3
Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.
基于广义(G'/G)展开法新方法的Boussinesq方程行波解
Springerplus. 2014 Jan 23;3:43. doi: 10.1186/2193-1801-3-43. eCollection 2014.