The Multi-resolution Haar Wavelets Collocation Procedure for Fractional Riccati Equations
Abstract
In this paper, we present a Haar wavelet collocation method (HWCM) for solving fractional Riccati equations. The primary goal of this study is to bypass the requirement of calculating the Jacobian of the nonlinear system of algebraic equations by using an iterative quasi-linearization technique. The Haar wavelet series is then utilized to approximate the first-order derivative, which is incorporated into the Caputo derivative framework to express the fractional-order derivative. This process transforms the nonlinear Riccati equation into a linear system of algebraic equations, which does not require calculating the Jacobian and can be efficiently solved using any standard linear solver. We evaluate the performance of HWCM on various forms of fractional Riccati equations, demonstrating its efficiency and accuracy. Compared to existing methods in the literature, our proposed HWCM produces more precise results, making it a valuable tool for solving fractional-order differential equations.
Recommended Citation
M. Ahsan et al., "The Multi-resolution Haar Wavelets Collocation Procedure for Fractional Riccati Equations," Physica Scripta, vol. 99, no. 11, article no. 115265, IOP Publishing; Royal Swedish Academy of Sciences, Nov 2024.
The definitive version is available at https://doi.org/10.1088/1402-4896/ad85a7
Department(s)
Mathematics and Statistics
Keywords and Phrases
collocation method; fractional Riccati equation; Haar wavelet; iterative quasilinearization technique
International Standard Serial Number (ISSN)
1402-4896; 0031-8949
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 IOP Publishing; Royal Swedish Academy of Sciences, All rights reserved.
Publication Date
01 Nov 2024
Comments
National Natural Science Foundation of China, Grant 12471497