Haar wavelet based numerical technique for the solutions of fractional advection diffusion equations

Volume 34, Issue 3, pp 217--233 https://dx.doi.org/10.22436/jmcs.034.03.02

Publication Date: March 18, 2024 Submission Date: July 21, 2023 Revision Date: December 16, 2023 Accteptance Date: February 08, 2024

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Authors

Sh. Ahmed - Department of Mathematics, Central University of Haryana, Mahendergarh-123029, India. Sh. Jahan - Department of Mathematics, Central University of Haryana, Mahendergarh-123029, India. K. S. Nisar - Department of Mathematics, College of Sciences and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia. - Saveetha School of Engineering, SIMATS, Chennai, India.

Abstract

In this article, a new numerical technique based on Haar wavelet is introduced to solve the time fractional advection diffusion equations (TFADEs). First we have constructed a generalized operational matrix of fractional order integration using Haar wavelet without taking block pulse functions into account. The fractional derivative in these problems is in the Caputo sense. In the proposed technique, the unknown function is approximated by truncated Haar wavelet series. The efficiency of the computational approach is examined and validated using particular test problems, and are compared with those of existing methodologies. The numerical results show that the proposed technique is computationally more efficient and yields high accuracy over those methodologies. The behaviour of solutions of fractional order \(\alpha\) and their graphical representation is shown by using MATLAB (R2022a) at various values.

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Keywords

• Advection diffusion equation
• fractional calculus
• Haar wavelet
• multi-resolution analysis
• error analysis

MSC

•  35Q79
•  65N35
•  42C40
•  26A33
•  35R11

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