Polynomial approximation to the solution of differential equations using nature inspired optimization techniques
Ratika Rastogi1, Om Prakash Misra2, Rajshree Mishra3
1Department of Mathematics, Government P.G. College, Madhya Pradesh, India
2School of Mathematics and Allied Sciences, Jiwaji University, Madhya Pradesh, India
3Department of Mathematics, Shrimant Madhavrao Scindia Government Model Science College, Madhya Pradesh, India
Keywords: differential equations, polynomials, differential evolution, particle swarm optimization
Abstract
The real life problems related to engineering and physical systems are theoretically studied using mathematical models and are generally formulated using linear and non-linear differential equations. This work proposes a numerical technique to find approximate solutions of differential equations utilizing polynomials as base approximation functions and metaheuristic optimization algorithms like Differential Evolution (DE) and Particle Swarm Optimization (PSO) for obtaining the optimal values of coefficients of the polynomials in order to get the desired approximate solution. The algorithms for the proposed method have been executed using MATLAB for computer programming. The effectiveness of the approach suggested in this paper is found to be better than or at least comparable to other numerical methods suggested earlier for solving differential equations.
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