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Quasilinearization–Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem

Authors: Kourosh Parand, Fatemeh Baharifard, Alireza Rezaei


In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Heat Transfer, nonlinear ODE, Quasilinearization method, Barycentric lagrange interpolation, fin problem

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