Petviashvilli's Method for the Dirichlet Problem

作者：Olson D; Shukla S; Simpson G; Spirn D^*

来源：Journal of Scientific Computing, 2016, 66(1): 296-320.

DOI：10.1007/s10915-015-0023-6

• Solitary waves
• Nonlinear waves
• Semilinear elliptic equations
• Iterative methods
• Global convergence

We examine Petviashvilli's 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 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.

• 出版日期2016-1