Numerical solution for high-order linear complex differential equations with variable coefficients

2017 ◽  
Vol 34 (5) ◽  
pp. 1645-1658 ◽  
Author(s):  
Faruk Düşünceli ◽  
Ercan Çelik
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Variable Coefficients ◽  
High Order ◽  
Linear Complex ◽  
Order Linear ◽  
Complex Differential Equations

scholarly journals A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Faezeh Toutounian ◽  
Emran Tohidi ◽  
Stanford Shateyi
Keyword(s):  
Differential Equations ◽  
Matrix Equation ◽  
Operational Matrix ◽  
Bernoulli Polynomials ◽  
High Order ◽  
Linear Complex ◽  
Order Linear ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Complex Differential Equations

This paper contributes a new matrix method for the solution of high-order linear complex differential equations with variable coefficients in rectangular domains under the considered initial conditions. On the basis of the presented approach, the matrix forms of the Bernoulli polynomials and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown Bernoulli coefficients are determined and thus the approximate solutions are obtained. Also, an error analysis based on the use of the Bernoulli polynomials is provided under several mild conditions. To illustrate the efficiency of our method, some numerical examples are given.

Solving systems of high-order linear ordinary differential equations with variable coefficients by means of exponential Chebyshev collocation method

2017 ◽  
Vol 8 (1-2) ◽  
pp. 40 ◽  
Author(s):  
Mohamed Ramadan ◽  
Kamal Raslan ◽  
Talaat El Danaf ◽  
Mohamed A. Abd Elsalam
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Variable Coefficients ◽  
High Order ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Linear Algebraic Equations

The purpose of this paper is to investigate the use of exponential Chebyshev (EC) collocation method for solving systems of high-order linear ordinary differential equations with variable coefficients with new scheme, using the EC collocation method in unbounded domains. The EC functions approach deals directly with infinite boundaries without singularities. The method transforms the system of differential equations and the given conditions to block matrix equations with unknown EC coefficients. By means of the obtained matrix equations, a new system of equations which corresponds to the system of linear algebraic equations is gained. Numerical examples are given to illustrative the validity and applicability of the method.

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