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Numerical Assessment Of The Brain Tumor Growth Model Via Fibonacci And Haar Wavelets

Author

Listed:
  • NAIED AHMAD NAYIED

    (Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu and kashmir, India)

  • FIRDOUS AHMAD SHAH

    (��Department of Mathematics, University of Kashmir, Anantnag 192101, Jammu and Kashmir, India)

  • KOTTAKKARAN SOOPPY NISAR

    (��Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia)

  • MUKHTAR AHMAD KHANDAY

    (Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu and kashmir, India)

  • SAIMA HABEEB

    (�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.

Suggested Citation

  • Naied Ahmad Nayied & Firdous Ahmad Shah & Kottakkaran Sooppy Nisar & Mukhtar Ahmad Khanday & Saima Habeeb, 2023. "Numerical Assessment Of The Brain Tumor Growth Model Via Fibonacci And Haar Wavelets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-17.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400170
    DOI: 10.1142/S0218348X23400170
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    Cited by:

    1. Manohara, G. & Kumbinarasaiah, S., 2024. "Numerical approximation of fractional SEIR epidemic model of measles and smoking model by using Fibonacci wavelets operational matrix approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 358-396.

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