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) |
|---|---|
| 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 |
Keywords
- Global convergence
- Iterative methods
- Nonlinear waves
- Semilinear elliptic equations
- Solitary waves
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Olson, D., Shukla, S., Simpson, G., & Spirn, D. (2016). Petviashvilli’s Method for the Dirichlet Problem. Journal of Scientific Computing, 66(1), 296-320. https://doi.org/10.1007/s10915-015-0023-6