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 Collocation for High-Order Differential Equations with Lidstone Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Francesco Costabile ◽  
Anna Napoli
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Collocation Method ◽  
Numerical Experiments ◽  
Recurrence Formula ◽  
High Order ◽  
Theoretical Results

A class of methods for the numerical solution of high-order differential equations with Lidstone and complementary Lidstone boundary conditions are presented. It is a collocation method which provides globally continuous differentiable solutions. Computation of the integrals which appear in the coefficients is generated by a recurrence formula. Numerical experiments support theoretical results.

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