A modified homotopy perturbation method for singular time dependent Emden–Fowler equations with boundary conditions
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In this paper, we propose a new modification of the homotopy perturbation method (HPM) for solving nonlinear and singular time-dependent Emden–Fowler-types equations with the Neumann and Dirichlet boundary conditions. We first transform the singular problem into an equivalent integral equation, and we then apply the HPM to obtain approximate series solution. This new modified HPM will be used without unknown constants while computing the successive solution components, and we also avoid solving a sequence of transcendental equations for the determination of the unknown constants. Moreover, the proposed technique is reliable enough to overcome the difficulty of the singular point at \(x=0\). Four illustrative examples are examined to demonstrate the accuracy and applicability of the proposed method.
KeywordsEmden–fowler equations Heat-type equations Wave-type equations Singular behavior Homotopy perturbation method
- 8.R. Singh, A.-M. Wazwaz, J. Kumar, An efficient semi-numerical technique for solving nonlinear singular boundary value problems arising in various physical models. Int. J. Compt. Math. (2015). doi: 10.1080/00207160.2015.1045888