Predictor homotopy analysis method and its application to some nonlinear problems |
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Institution: | 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract: | The purpose of this paper is to present a kind of analytical method so-called Predictor homotopy analysis method (PHAM) to predict the multiplicity of the solutions of nonlinear differential equations with boundary conditions. This method is very useful especially for those boundary value problems which admit multiple solutions and furthermore is capable to calculate all branches of the solutions simultaneously. As illustrative examples, the method is checked by the model of mixed convection flows in a vertical channel and a nonlinear model arising in heat transfer which both admit multiple (dual) solutions. |
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