NUMERICAL ASSESSMENT OF THE BRAIN TUMOR GROWTH MODEL VIA FIBONACCI AND HAAR WAVELETS

Author:

NAYIED NAIED AHMAD1,SHAH FIRDOUS AHMAD2,NISAR KOTTAKKARAN SOOPPY3,KHANDAY MUKHTAR AHMAD1,HABEEB SAIMA4

Affiliation:

1. Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu and kashmir, India

2. Department of Mathematics, University of Kashmir, Anantnag 192101, Jammu and Kashmir, India

3. Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia

4. Rufaida College of Nursing, Jamia Hamdard, New Delhi 110019, India

Abstract

The main goal of this paper is to present a novel numerical scheme based on the Fibonacci wavelets for solving the brain tumor growth model governed by the Burgess equation. At the first instance, the Fibonacci-wavelet-based operational matrices of integration are obtained by following the well-known Chen–Hsiao technique. These matrices play a vital role in converting the said model into an algebraic system, which could be handled with any standard numerical method. To access the effect of medical treatment over the brain tumor growth, we have investigated both the linear and nonlinear cases of Burgess equation. The nonlinearity arising in the Burgess equation is handled by invoking the quasilinearization technique. In order to compare the efficiency of the Fibonacci-wavelet-based numerical technique, we formulated an analogous numerical scheme based on the Haar wavelets. Subsequently, both the methods are testified on several test problems and it is demonstrated that the Fibonacci wavelet method yields a much more stable solution and a better approximation than the Haar wavelet method.

Funder

Prince Sattam bin Abdulaziz University

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

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