Open AccessNUMERICAL STUDY OF HEAT TRANSFERS IN TISSUES DURING HYPERTHERMIA USING MODIFIED BERNSTEIN POLYNOMIALS
Author(s) -
Vineet K. Srivastava
Publication year - 2020
Publication title -
journal of mathematical sciences and computational mathematics
Language(s) - English
Resource type - Journals
eISSN - 2688-8300
pISSN - 2644-3368
DOI - 10.15864/jmscm.2108
Subject(s) - mathematics , bernstein polynomial , discretization , galerkin method , boundary value problem , polynomial basis , matrix polynomial , mathematical analysis , polynomial , algebraic equation , homotopy analysis method , homotopy , finite element method , pure mathematics , physics , nonlinear system , quantum mechanics , thermodynamics
In the present article, we use modified Bernstein polynomial (B–polynomial) as a basis for the numerical approximation of heat transfer in hyperthermia treatment. A set of continuous polynomials over the spatial domain is use to expand the desired solution using discretization in time variable only. The Galerkin method is use to determine the expansion coefficients to construct initial trial functions. The system of equations has been solved using fourth–order Runge-Kutta method. The accuracy of the solutions is dependent on the size of the B–polynomial basis set. Also, Homotopy Perturbation Method has been applied to solve Matrix form of initial value differential equations which is transformed from boundary value differential equation of desired problem by using central difference scheme. The results thus obtained are in very good agreement with the previous results and it is presented graphically.