scholarly journals Taylor collocation method for systems of high-order linear differential–difference equations with variable coefficients

2013 ◽  
Vol 4 (1) ◽  
pp. 117-125 ◽  
Author(s):  
Elçin Gökmen ◽  
Mehmet Sezer
Keyword(s):  
Collocation Method ◽  
Difference Equations ◽  
Variable Coefficients ◽  
High Order ◽  
Order Linear ◽  
Linear Differential

Numerical Solutions of Systems of High-Order Linear Differential-Difference Equations with Bessel Polynomial Bases

2011 ◽  
Vol 66 (8-9) ◽  
pp. 519-532 ◽  
Author(s):  
Șuayip Yüzbași ◽  
Niyazi Șahin ◽  
Ahmet Yıldırımb
Keyword(s):  
Difference Equations ◽  
Numerical Solutions ◽  
Variable Coefficients ◽  
High Order ◽  
Numerical Examples ◽  
Order Linear ◽  
Collocation Points ◽  
Bessel Polynomial ◽  
Polynomial Bases ◽  
Linear Differential

Abstract In this paper, a numerical matrix method, which is based on collocation points, is presented for the approximate solution of a system of high-order linear differential-difference equations with variable coefficients under the mixed conditions in terms of Bessel polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in MATLAB v7.6.0 (R2008a).

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.

scholarly journals Fibonacci Collocation Method for Solving High-Order Linear Fredholm Integro-Differential-Difference Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ayşe Kurt ◽  
Salih Yalçınbaş ◽  
Mehmet Sezer
Keyword(s):  
Approximate Solution ◽  
Collocation Method ◽  
Difference Equations ◽  
Numerical Experiments ◽  
High Order ◽  
Fibonacci Polynomials ◽  
Order Linear

A new collocation method based on the Fibonacci polynomials is introduced for the approximate solution of high order-linear Fredholm integro-differential-difference equations with the mixed conditions. The proposed method is analyzed to show the convergence of the method. Some further numerical experiments are carried out to demonstrate the method.

scholarly journals Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammed Çetin ◽  
Mehmet Sezer ◽  
Coşkun Güler
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
High Order ◽  
Linear Differential Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
Lucas Polynomials ◽  
Linear Algebraic Equations ◽  
Linear Differential

An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written inMapleandMatlab.

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