The Method of Particular Solutions for Solving Nonlinear Poisson Problems
Based on the recent development in the method of particular solutions, we re-exam three approaches using different basis functions for solving nonlinear Poisson problems. We further propose to simplify the solution procedure by removing the insolvency condition when the radial basis functions are augmented with high order polynomial basis functions. We also specify the deficiency of some of these methods and provide necessary remedy. The traditional Picard method is introduced to compare with the recent proposed methods using MATLAB optimization toolbox solver for solving nonlinear Poisson equations. Ranking on these three approaches are given based on the results of numerical experiment
Computers & Mathematics with Applications
(2018). The Method of Particular Solutions for Solving Nonlinear Poisson Problems. Computers & Mathematics with Applications, 77(2), 501-513.
Available at: https://aquila.usm.edu/fac_pubs/15634