scholarly journals A numerical approach for solving the high-order linear singular differential–difference equations

2011 ◽  
Vol 62 (5) ◽  
pp. 2289-2303 ◽  
Author(s):  
Şuayip Yüzbaşı
Keyword(s):  
Difference Equations ◽  
Numerical Approach ◽  
High Order ◽  
Order Linear

A Numerical Approach for Solving High-Order Linear Delay Volterra Integro-Differential Equations

2018 ◽  
Vol 15 (05) ◽  
pp. 1850042 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Murat Karaçayır
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Numerical Approach ◽  
High Order ◽  
Inner Product ◽  
Present Scheme ◽  
Order Linear ◽  
Linear Delay ◽  
Residual Correction

In this study, a numerical method is proposed to solve high-order linear Volterra delay integro-differential equations. In this approach, we assume that the exact solution can be expressed as a power series, which we truncate after the [Formula: see text]-st term so that it becomes a polynomial of degree [Formula: see text]. Substituting the unknown function, its derivatives and the integrals by their matrix counterparts, we obtain a vector equivalent of the equation in question. Applying inner product to this vector with a set of monomials, we are left with a linear algebraic equation system of [Formula: see text] unknowns. The approximate solution of the problem is then computed from the solution of the resulting linear system. In addition, the technique of residual correction, whose aim is to increase the accuracy of the approximate solutions by estimating the error of those solutions, is discussed briefly. Both the method and this technique are illustrated with several examples. Finally, comparison of the present scheme with other methods is made wherever possible.

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.

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