scholarly journals Numerical Solution of Nonlinear Singular Ordinary Differential Equations Arising in Biology Via Operational Matrix of Shifted Legendre Polynomials

2012 ◽  
Vol 1 (1) ◽  
pp. 15-19 ◽  
Author(s):  
K. Maleknejad ◽  
E. Hashemizadeh
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Legendre Polynomials ◽  
Operational Matrix ◽  
Shifted Legendre Polynomials

scholarly journals Wang-Ball Polynomials for the Numerical Solution of Singular Ordinary Differential Equations

2021 ◽  
pp. 941-949
Author(s):  
Ahmed Kherd ◽  
Azizan Saaban ◽  
Ibrahim Eskander Ibrahim Fadhel
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Operational Matrix ◽  
Second Order ◽  
Operational Matrices ◽  
Second Order Equations

This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions.

Numerical solution for singular differential equations using Haar wavelet

2020 ◽  
Vol 11 (05) ◽  
pp. 2050038
Author(s):  
Shitesh Shukla ◽  
Manoj Kumar
Keyword(s):  
Differential Equations ◽  
Error Analysis ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
System Analysis ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Basic Tool ◽  
Singular Differential Equations ◽  
Haar Function

The aim of this paper is to obtain the numerical solution of singular ordinary differential equations using the Haar-wavelet approach. The proposed method is mathematically simple and provides highly accurate solutions. In this method, we derive the Haar operational matrix using Haar function. Haar operational matrix is a basic tool and applied in system analysis to evaluate the numerical solution of differential equations. The convergence of the proposed method is discussed through its error analysis. To illustrate the efficiency of this method, solutions of four singular differential equations are obtained.

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