A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation

Haifa Bin Jebreen and Ioannis Dassios
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Haifa Bin Jebreen: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Ioannis Dassios: FRESLIPS, University College Dublin, D04 V1W8 Dublin, Ireland

Mathematics, 2022, vol. 10, issue 9, 1-14

Abstract: This paper is devoted to the wavelet Galerkin method to solve the Fractional Riccati equation. To this end, biorthogonal Hermite cubic Spline scaling bases and their properties are introduced, and the fractional integral is represented based on these bases as an operational matrix. Firstly, we obtain the Volterra integral equation with a weakly singular kernel corresponding to the desired equation. Then, using the operational matrix of fractional integration and the Galerkin method, the corresponding integral equation is reduced to a system of algebraic equations. Solving this system via Newton’s iterative method gives the unknown solution. The convergence analysis is investigated and shows that the convergence rate is O ( 2 − s ) . To demonstrate the efficiency and accuracy of the method, some numerical simulations are provided.

Keywords: Galerkin method; wavelet; fractional equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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