THE METHOD OF PARTICULAR SOLUTIONS FOR FINDING CRITICAL DOMAINS FOR QUENCHING PROBLEMS

In this work, the method of particular solutions (MPS) has been used for solving nonlinear Poisson-type problems defined on different geometries. The polyharmonic splines is used as the basis function so that no shape parameter is needed in the solution process. The MPS is also applied to compute the sizes of critical domains of different shapes for a quenching problem and compared with the sizes of critical domains obtained from some other numerical methods. Numerical examples are presented to show the efficiency and accuracy of the method.