Operational matrix method for solving Riccati differential equation by using hybrid third kind Chebyshev polynomials and block-pulse functions

2021 ◽  
Vol 19 (2) ◽  
pp. 161
Author(s):  
Reza Jafari
Keyword(s):  
Differential Equation ◽  
Chebyshev Polynomials ◽  
Matrix Method ◽  
Operational Matrix ◽  
Riccati Differential Equation ◽  
Operational Matrix Method ◽  
Block Pulse Functions

scholarly journals Hybrid functions approach for the fractional Riccati differential equation

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2453-2463 ◽  
Author(s):  
Khosrow Maleknejad ◽  
Leila Torkzadeh
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equations ◽  
Efficient Method ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Operational Matrices ◽  
Riccati Differential Equation ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Fractional Differential

In this paper, we state an efficient method for solving the fractional Riccati differential equation. This equation plays an important role in modeling the various phenomena in physics and engineering. Our approach is based on operational matrices of fractional differential equations with hybrid of block-pulse functions and Chebyshev polynomials. Convergence of hybrid functions and error bound of approximation by this basis are discussed. Implementation of this method is without ambiguity with better accuracy than its counterpart other approaches. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

Numerical solution of Riccati equation using operational matrix method with Chebyshev polynomials

2015 ◽  
Vol 08 (02) ◽  
pp. 1550020
Author(s):  
Yalçın Öztürk ◽  
Mustafa Gülsu
Keyword(s):  
Approximate Solution ◽  
Riccati Equation ◽  
Chebyshev Polynomials ◽  
Matrix Method ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Chebyshev Series ◽  
Numerical Examples ◽  
Operational Matrix Method

In this paper, we present numerical technique for solving the Riccati equation by using operational matrix method with Chebyshev polynomials. The method consists of expanding the required approximate solution as truncated Chebyshev series. Using operational matrix method, we reduce the problem to a set of algebraic equations. Some numerical examples are given to demonstrate the validity and applicability of the method. The method is easy to implement and produces very accurate results.

Haar Wavelet Operational Matrix Method for the Numerical Solution of Fractional Order Differential Equations

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Firdous A. Shah ◽  
R. Abbas
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Matrix Method ◽  
Present Method ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Operational Matrix Method ◽  
Fractional Order Differential Equations ◽  
Block Pulse Functions

AbstractIn this paper, we propose a new operational matrix method of fractional order integration based on Haar wavelets to solve fractional order differential equations numerically. The properties of Haar wavelets are first presented. The properties of Haar wavelets are used to reduce the system of fractional order differential equations to a systemof algebraic equationswhich can be solved numerically byNewton’s method.Moreover, the proposed method is derived without using the block pulse functions considered in open literature and does not require the inverse of the Haar matrices. Numerical examples are included to demonstrate the validity and applicability of the present method.

Sign in / Sign up

Export Citation Format

Share Document