Numerical Solution of Dirichlet Boundary Value Problems for Partial Differential Equations Using Quantum-Behaved Particle Swarm Optimization with Random Gaussian Function

A new mesh-based algorithm to solve partial differential equations (PDEs) using quantum-behaved particle swarm optimization (QPSO) with random Gaussian function and random median filter is proposed in this paper. The random Gaussian function behaves as a mutation operator of QPSO to escape from local minima, and the random median filter accelerates the convergence of QPSO. It provides accurate results for Dirichlet boundary value problems of both linear and nonlinear single PDEs in two space dimensions.