Input Variant Particle Swarm Optimization for Solving Ordinary and Partial Differential Equations with Constraints

Abstract

In this paper, a novel method for solving ordinary and partial differential equations is presented. The proposed method gives a numerical solution based on an input variant particle swarm optimization; where each particle, has a dimension equal to the number of expected solutions. The proposed method also overcomes the problem of considering many constraints (initial and boundary conditions) for the solution.The main motivation of this paper, is to find a solver that is accurate, fast and can handle many constrains as well as many variables. This method is tested over many systems of ordinary and partial differential equations. Further, the proposed is compared with some leading state of the art techniques.