A Comparative Analysis of Convergence Techniques for the Homotopy Perturbation Method to Solve the Burgers’ Equation in One Dimension
Keywords:
Homotopy separation of Variables, Modified Homotopy Perturbation Method, Burger's Equation, Nonlinear partial differential equationsAbstract
This paper aims to select suitable initial approximations that increase the convergence rate and reduce the size of the accounts for the homotopy perturbation method (HPM). The study was conducted using two methods: the homotopy separation of variables (HSV) and the modified homotopy perturbation method (MHPM). The methods were tested on three problems of the Burgers’ equation. Although the modified methods had the same number of iterations, the results showed that, in one example, the magnitude of error in the MHPM was significantly lower. Therefore, the MHPM is more effective than the HSV. Thus, the selection of the optimal initial approximation has an impact on improving the performance of the HPM.
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