Title: Cell-like P-systems coupled with rules of particle swarm optimisation to solve Blasius differential equation
Authors: Garima Singh; Kusum Deep
Addresses: Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee – 247667, India ' Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee – 247667, India
Abstract: In this paper, a non-traditional approach is presented to numerically solve the well-known differential equation, namely Blasius equation, by modelling it as a nonlinear optimisation problem, in which parameters of the nonlinear approximation function satisfying the boundary conditions are identified, by minimising the error. The optimisation methodology involves the use of cell-like P-systems, in which hierarchical membrane structures use the evolution rules of particle swarm optimisation. A comparative implementation of five such P-systems is used to solve the Blasius equation. It is concluded that all the five algorithms provide solutions close to the exact solution and well within the specified lower and upper bounds. It is suggested that the presented approach can be easily extended to solve a wide range of similar problems.
Keywords: particle swarm optimisation; PSO; cell-like P-systems; Blasius differential equations; membrane algorithms; modelling; nonlinear optimisation.
International Journal of Swarm Intelligence, 2016 Vol.2 No.1, pp.87 - 96
Received: 20 Oct 2015
Accepted: 10 Dec 2015
Published online: 28 Jun 2016 *