Proper Generalized Decomposition Method for Solving Fisher-Type Equation and Heat Equation |
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Authors: | Chukwuemeke William Isaac |
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Affiliation: | 1.Dept. of Mechanical Engineering,University of Ibadan,Ibadan,Nigeria |
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Abstract: | A model reduction technique—the Proper Generalized Decomposition (PGD) for solving time dependent and multidimensional parameters is reviewed and applied to both the Fisher-type equations and the heat equation. Space-time discretization and separated representation technique for obtaining fast convergence computation while maintaining real time is detailed. Three situations of the Fisher-type equation are solved by the PGD and the results show a perfect agreement with the exact solutions. The source term of the heat equation is given a Huxley source and the thermal diffusivity is taken to be linearly dependent of the spatial parameter. The results show how the Fisher-type equation finds application to the heat equation and that the PGD method allows a perfect representation of the temperature distribution defined in a 5-D tensorial product space and time. |
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