The Least Square Method for Systems of Linear Ordinary Differential Equations

2019 ◽  
Vol 59 (6) ◽  
pp. 915-925 ◽  
Author(s):  
A. A. Abramov ◽  
L. F. Yukhno
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Least Square Method ◽  
Least Square ◽  
Linear Ordinary Differential Equations

scholarly journals Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method

2020 ◽  
Vol 33 (4) ◽  
pp. 59
Author(s):  
Israa M. Salman ◽  
Eman A. Abdul-Razzaq
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Nonlinear Delay

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

Least Square Methods Based on Control Points of Said Ball Curves for Solving Ordinary Differential Equations

2021 ◽  
Vol 12 (3) ◽  
pp. 2597-2607
Author(s):  
Abdul Hadi Bhatti Et.al
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Least Squares ◽  
Ordinary Differential Equations ◽  
Least Square ◽  
Control Points ◽  
Residual Function ◽  
Numerical Examples ◽  
Linear Ordinary Differential Equations

This paper presents the use of Said Ball curve’s control points to approximate the solutions of linear ordinary differential equations (ODEs). Least squares methods (LSM) is proposed to find the control points of Said Ball curves by minimizing the error of residual function.The residual error is measured by taking the sum of squares of the Said Ball curve’s control points of the residual function. Then the approximate solution of ODEs is obtained by minimizing residual error.Two numerical examples are given in term of error and compared with the exact solution to demonstrate the efficiency of the proposed method.

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