Quasilinearization–Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem
Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand
Abstract:
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: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334161
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