Petviashvilli’s Method for the Dirichlet Problem
| Autor: | Gideon Simpson, Derek A Olson, Daniel Spirn, Soumitra Shukla |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Dirichlet problem Numerical Analysis Sequence Iterative method Applied Mathematics 010102 general mathematics General Engineering 01 natural sciences Domain (mathematical analysis) 010305 fluids & plasmas Theoretical Computer Science Local convergence Computational Mathematics symbols.namesake Computational Theory and Mathematics Bounded function Dirichlet boundary condition 0103 physical sciences Convergence (routing) symbols 0101 mathematics Software Mathematics |
| Zdroj: | Journal of Scientific Computing. 66:296-320 |
| ISSN: | 1573-7691 0885-7474 |
| DOI: | 10.1007/s10915-015-0023-6 |
| Popis: | We examine Petviashvilli's method for solving the equation $$ \phi - \Delta \phi = |\phi |^{p-1} \phi $$?-Δ?=|?|p-1? on a bounded domain $$\Omega \subset \mathbb {R}^d$$Ω?Rd with Dirichlet boundary conditions. We prove a local convergence result, using spectral analysis, akin to the result for the problem on $$\mathbb {R}$$R by Pelinovsky and Stepanyants in [16]. We also prove a global convergence result by generating a suite of nonlinear inequalities for the iteration sequence, and we show that the sequence has a natural energy that decreases along the sequence. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink