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A reduction algorithm for sublinear Dirichlet problems

โœ Scribed by Jorge Cossio; Sheldon Lee; John M. Neuberger

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
454 KB
Volume
47
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

We consider a sublinear elliptic BVP on the unit square and recall proofs for the existence of five solutions. Previous algorithms which follow the constructive nature of the existence proofs are able to find four of these solutions. The fifth solution follows from an application of the Lyapunov-Schmidt reduction method. We provide here a new algorithm for approximating this solution which realizes the reduction minimizing function. We implement this new algorithm using an orthonormal finite sub-basis of eigenfunctions.

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