Generalized wavelet method for solving fractional bioheat transfer model during hyperthermia treatment

摘要

In this study, we develop a generalized wavelet-based collocation method to solve the fractional Pennes bioheat transfer model during hyperthermia treatment. Unlike the existing operational matrix methods based on orthogonal functions, we formulate the Haar wavelet operational matrices of general order integration without using the block pulse functions. Consequently, the governing problem is transformed into an equivalent system of algebraic equations, which can be tackled with any classical method. Some prime features of the proposed method include no requirement of the inverse of the Haar matrices, no need to convert the boundary value problem into the initial-value problem, which in turn eliminates the possibility of unstable solutions. The proposed technique is testified for different values of fractional parameter alpha and is observed that as the fractional parameter alpha increases, the tissue temperature at the target region also increases appreciably. Moreover, the obtained results also indicate that the overall time taken to attain the hyperthermia temperature for the fractional model is comparatively less than the classical bioheat model.