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Petviashvilli's Method for the Dirichlet Problem
We examine the Petviashvilli method for solving the equation on a bounded domain
with Dirichlet boundary conditions. We prove a local convergence result, using
spectral analysis, akin to the result for the problem on by
Pelinovsky & Stepanyants, 2004. 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.Comment: 24 pages, 7 figures, shortened for publication with some corrections.
See v1 for more detailed proofs of the local convergenc