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Journal article
Petviashvilli’s Method for the Dirichlet Problem
Journal of scientific computing, v 66(1)
2016
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Abstract
We examine Petviashvilli’s method for solving the equation
ϕ
-
Δ
ϕ
=
|
ϕ
|
p
-
1
ϕ
on a bounded domain
Ω
⊂
R
d
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.
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Details
- Title
- Petviashvilli’s Method for the Dirichlet Problem
- Creators
- D. Olson - University of MinnesotaS. Shukla - University of MinnesotaG. Simpson - Drexel UniversityD. Spirn - University of Minnesota
- Publication Details
- Journal of scientific computing, v 66(1)
- Publisher
- Springer US
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000368167500013
- Scopus ID
- 2-s2.0-84953637551
- Other Identifier
- 991019168956304721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied