Determining approximate solution of partial differential equations using radial basis function model trained with parallel symbiotic organisms search algorithm

Abstract

SummaryPartial differential equations (PDEs) find extensive applications in geophysics (weather and climate modeling), astrophysics, and quantum mechanics. Solving PDEs by the conventional methods at times becomes difficult due to the complexity involved in these real‐world problems. Thus instead of an exact solution determining an approximate solution is also helpful for solving the problems. Here a model based on radial basis function (RBF) trained with parallel symbiotic organism search (PSOS) optimization is proposed to find out an approximate solution. The PSOS is a nature‐inspired optimization algorithm that ensures better accuracy due to the potential exploration of agents in the search space. Simultaneously, the computational complexity of this algorithm is low due to inbuilt parallelism. Simulation studies are reported for five real applications of PDEs: 2D modified Helmholtz equation, Poisson problem with Dirichlet boundary condition, elliptic PDE equation, and two convection‐diffusion equations. Comparison is carried out with the same RBF model parameters trained with parallel social spider optimization, original symbiotic organisms search algorithm, real coded genetic algorithm, and particle swarm optimization. The proposed model achieves minimum root mean square errors in most of the cases and achieves it with lower run time compared to the existing algorithms.