Abstract
We examine Petviashvilli’s method for solving the equation ϕ-Δϕ=|ϕ|p-1ϕ on a bounded domain Ω⊂Rd with Dirichlet boundary conditions. We prove a local convergence result, using spectral analysis, akin to the result for the problem on 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.
Original language | English (US) |
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Pages (from-to) | 296-320 |
Number of pages | 25 |
Journal | Journal of Scientific Computing |
Volume | 66 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2016 |
Bibliographical note
Publisher Copyright:© 2015, Springer Science+Business Media New York.
Keywords
- Global convergence
- Iterative methods
- Nonlinear waves
- Semilinear elliptic equations
- Solitary waves