Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations

Abstract

Abstract. In this paper, numerical solutions of Riccati and fractional Riccati differential equations are obtained by the Haar wavelet collocation method. An operational matrix of integration based on the Haar wavelet is established, and the procedure for applying the matrix to solve these equations. The fundamental idea of Haar wavelet method is to convert the proposed differential equations into a group of non-linear algebraic equations. The accuracy of approximate solution can be further improved by increasing the level of resolution and an error analysis is computed. The examples are given to demonstrate the fast and flexibility of the method. The results obtained are in good agreement with the exact in comparison with existing ones and it is shown that the technique introduced here is robust, easy to apply and is not only enough accurate but also quite stable.

An Effective Computational Scheme for Solving Various Mathematical Fractional Differential Models via Non-Dyadic Haar Wavelets Fractional Differential Models via Non-Dyadic Haar Wavelets

“…Due to this, with the help of HS3W, the rate of convergence of the solution has increased. With dilation factor three, the family of HS3W with detailed information about Haar function, father wavelet, and symmetric and antisymmetric mother wavelets is provided below (Arora et al, 2020;Shiralashetti & Deshi, 2016).…”

A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations

“…Namely, Bujurke et al [10][11][12] used the single term Haar wavelet series for the numerical solution of stiff systems from nonlinear dynamics, nonlinear oscillator equations and Sturm-Liouville problems. Shiralashetti et al [13][14][15][16]18] applied for the numerical solution of Klein?Gordan equations, multi-term fractional differential equations, singular initial value problems,nonlinear Fredholm integral equations, Riccati and Fractional Riccati Differential Equations. Shiralashetti et al [17] have introduced the adaptive gird Haar wavelet collocation method for the numerical solution of parabolic partial differential equations.…”

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

“…Siraj-ul-Islam et al [23] proposed for the numerical solution of second order boundary value problems. Shiralashetti et al [24][25][26][27] applied for the numerical solution of KleinGordan equations, multi-term fractional differential equations, singular initial value problems and Riccati and Fractional Riccati Differential Equations. Shiralashetti et al [28] have introduced the adaptive gird Haar wavelet collocation method for the numerical solution of parabolic partial differential equations.…”