Particle Swarm Optimization for Solving Sine-Gordan Equation

Abstract

The term 'optimization' refers to the process of maximizing the beneficial attributes of a mathematical function or system while minimizing the unfavorable ones. The majority of real-world situations can be modelled as an optimization problem. The complex nature of models restricts traditional optimization techniques to obtain a global optimal solution and paves the path for global optimization methods. Particle Swarm Optimization is a potential global optimization technique that has been widely used to address problems in a variety of fields. The idea of this research is to use exponential basis functions and the particle swarm optimization technique to find a numerical solution for the Sine-Gordan equation, whose numerical solutions show the soliton form and has diverse applications. The implemented optimization technique is employed to determine the involved parameter in the basis functions, which was previously approximated as a random number in the work reported till now in the literature. The obtained results are comparable with the results obtained in the literature. The work is presented in the form of figures and tables and is found encouraging.

Mathematical Models of Wound Healing and Tissue Regeneration: Insights with Numerical Solution

“…The limited usage of this B-spline can be attributed to the unknown parameter involved that play a major role in finding the numerical solution. To deal with the unknown parameter authors have used the optimization as a tool to obtain the parameter that has proven to be an effective way to obtain the solution of PDE [31,32] . The present study used the widely recognized PSO optimization technique to determine the tension parameter that could results in the minimum error.…”