The approximate solution of high-order linear difference equations with variable coefficients in terms of Taylor polynomials

2005 ◽  
Vol 168 (1) ◽  
pp. 76-88 ◽  
Author(s):  
Mustafa Gülsu ◽  
Mehmet Sezer
Keyword(s):  
Approximate Solution ◽  
Difference Equations ◽  
Variable Coefficients ◽  
High Order ◽  
Linear Difference Equations ◽  
Order Linear ◽  
Taylor Polynomials

scholarly journals Polynomial approach for the most general linear Fredholm integrodifferential-difference equations using Taylor matrix method

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Mehmet Sezer ◽  
Mustafa Gülsu
Keyword(s):  
Approximate Solution ◽  
Difference Equations ◽  
Taylor Series ◽  
Matrix Method ◽  
Variable Coefficients ◽  
General Linear ◽  
Matrix Equations ◽  
Taylor Coefficients ◽  
Taylor Polynomials ◽  
The Given

A Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This method transforms the given general linear Fredholm integrodifferential-difference equations and the mixed conditions to matrix equations with unknown Taylor coefficients. By means of the obtained matrix equations, the Taylor coefficients can be easily computed. Hence, the finite Taylor series approach is obtained. Also, examples are presented and the results are discussed.

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.

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).

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