A pseudo-spectral solution of 2-parameter Bratu's equation
type: Item
instance of: scholarly article
title: A pseudo-spectral solution of 2-parameter Bratu's equation
zbMATH Open document ID: 0713.65067
DOI: 10.1007/BF00373799
published in: Computational Mechanics
publication date: 1990-01-01T00:00:00Z
review text: A simple pseudo-spectral (collocation type) method is used to study the boundary value problem: \(\frac{\partial^ 2u}{\partial x^ 2}+\frac{\partial^ 2u}{\partial y^ 2}+\lambda \exp (\frac{u}{1+\epsilon u})=0,\) \(0\leq | x|\), \(| y| \leq 1\), \(u(\pm 1,y)=u(x,\pm 1)\) where \(\lambda\),\(\epsilon\) are parameters. The resulting nonlinear set of algebraic equations is solved using a constant-arc type continuation method. The present algorithm is capable of successfully obtaining the various turning points in both \(\lambda\)- u(0,0) curves as well as \(\epsilon\)-u(0,0) curves.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 4174269
zbMATH Keywords: 2-parameter Bratu's equation
zbMATH Keywords: pseudo-spectral method
zbMATH Keywords: collocation
zbMATH Keywords: constant-arc type continuation method
zbMATH Keywords: algorithm
zbMATH Keywords: turning points
author: Rakesh K. Kapania
describes a project that uses: PLTMGC
MaRDI profile type: Publication
cites work: PLTMGC: A Multigrid Continuation Program for Parameterized Nonlinear Elliptic Systems
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description: scientific article; zbMATH DE number 4174269