Numerical Solution of Lienard Equation Using Hybrid Heuristic Computation
Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, Ihsanul Haq · 2013
2 Abstract: In this paper, a hybrid heuristic computing technique, stochastic in nature, is used for obtaining an approximate numerical solution of the Lienard equation. The proposed technique converts the nonlinear differential equation into an equivalent global error minimization problem. A trial solution is developed using a fitness function with unknown adaptable parameters. The memetic computation or hybrid genetic algorithms (HGAs) combining genetic algorithm (GA) with interior point algorithm (IPA), active set algorithm (ASA) and pattern search (PS) is used to solve the minimization problem and to obtain the unknown adaptable parameters. The accuracy and efficacy of the proposed technique is illustrated by considering the Lienard's equation with two special cases. Comparison of numerical results is made with the exact solution and two important deterministic standard methods, including variational iteration method (VIM) and differential transform method (DTM). The comparison of numerical results validate the effectiveness and viability of the suggested technique. The results obtained by the proposed method are found to be in excellent agreement with the exact solution.