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A pseudo-spectral solution of 2-parameter Bratu’s equation. (English) Zbl 0713.65067

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.
Reviewer: L.G.Vulkov

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
35J65 Nonlinear boundary value problems for linear elliptic equations

Software:

PLTMGC
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Full Text: DOI

References:

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