scholarly journals A Reliable Method for Solving Fractional Sturm–Liouville Problems

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 176 ◽  
Author(s):  
M. Khashshan ◽  
Muhammed Syam ◽  
Ahlam Al Mokhmari
Keyword(s):  
Matrix Method ◽  
Reliable Method ◽  
Operational Matrix ◽  
Liouville Problem ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Sturm Liouville

In this paper, a reliable method for solving fractional Sturm–Liouville problem based on the operational matrix method is presented. Some of our numerical examples are presented.

scholarly journals Fractional Order Operational Matrix Method for Solving Two-Dimensional Nonlinear Fractional Volterra Integro-Differential Equations

2021 ◽  
Vol 45 (4) ◽  
pp. 571-585
Author(s):  
AMIRAHMAD KHAJEHNASIRI ◽  
◽  
M. AFSHAR KERMANI ◽  
REZZA EZZATI ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Order ◽  
Volterra Integral Equation ◽  
Matrix Method ◽  
Operational Matrix ◽  
Basis Functions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Operational Matrix Method

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of the fractional order integration and use it to solve the two-dimensional fractional Volterra integro-differential equations. The method is described and illustrated with numerical examples. Also, we give the error analysis.

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.

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

2017 ◽  
Vol 10 (03) ◽  
pp. 1750053 ◽  
Author(s):  
Yalçın Öztürk ◽  
Mustafa Gülsu
Keyword(s):  
Chebyshev Polynomials ◽  
Matrix Method ◽  
Numerical Scheme ◽  
Operational Matrix ◽  
Abel Equation ◽  
Operational Method ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Nonlinear Algebraic Equations

In this paper, we present a numerical scheme for solving the Abel equation. The approach is based on the shifted Chebyshev polynomials together with operational method. We reduce the problem to a set of nonlinear algebraic equations using operational matrix method. In addition, convergence analysis of the method is presented. Some numerical examples are given to demonstrate the validity and applicability of the method. The only a small number of Chebyshev polynomials is needed to obtain a satisfactory result.

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

Haar wavelet operational matrix method for system of fractional nonlinear differential equations

2017 ◽  
Vol 15 (05) ◽  
pp. 1750043 ◽  
Author(s):  
Umer Saeed
Keyword(s):  
Differential Equations ◽  
Reliable Method ◽  
Nonlinear Differential Equations ◽  
Operational Matrix ◽  
Implementation Process ◽  
Haar Wavelet ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Operational Matrix Method ◽  
Fractional Differential

In this paper, we present a reliable method for solving system of fractional nonlinear differential equations. The proposed technique utilizes the Haar wavelets in conjunction with a quasilinearization technique. The operational matrices are derived and used to reduce each equation in a system of fractional differential equations to a system of algebraic equations. Convergence analysis and implementation process for the proposed technique are presented. Numerical examples are provided to illustrate the applicability and accuracy of the technique.

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