Fibonacci wavelet method for solving Pennes bioheat transfer equation

Abstract

In this paper, we develop an efficient wavelet method based on the Fibonacci polynomials for solving the Pennes bioheat transfer equation. The formulation of the proposed technique is started with the construction of Fibonacci wavelets by using Fibonacci polynomials and then applying spectral collocation technique to transform the given problem into a system of an algebraic equation, that can be solved using the Newton method. Some results related to error estimate and convergence analysis of the proposed scheme are also investigated. The applicability and accuracy of the present technique are elucidated by a comparison with the exact solution and those of the other methods found in the recent literature. The obtained results show that the proposed technique is an effective tool for solving Pennes bioheat transfer equations and can also be used for solving similar types of various partial differential equations numerically.