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).

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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