scholarly journals Polynomial spline collocation methods for second-order Volterra integrodifferential equations

2004 ◽  
Vol 2004 (56) ◽  
pp. 3011-3022 ◽  
Author(s):  
Edris Rawashdeh ◽  
David Mcdowell ◽  
Leela Rakesh
Keyword(s):  
Integrodifferential Equation ◽  
Polynomial Spline ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Initial Value ◽  
Volterra Integrodifferential Equation

We have presented a method for the construction of an approximation to the initial-value second-order Volterra integrodifferential equation (VIDE). The polynomial spline collocation methods described here give a superconvergence to the solution of the equation.

scholarly journals The stability of collocation methods for VIDEs of second order

2005 ◽  
Vol 2005 (7) ◽  
pp. 1049-1066 ◽  
Author(s):  
Edris Rawashdeh ◽  
Dave McDowell ◽  
Leela Rakesh
Keyword(s):  
Differential Equation ◽  
Jordan Block ◽  
Solution Procedure ◽  
Polynomial Spline ◽  
Second Order ◽  
Collocation Methods ◽  
Spline Functions ◽  
Stability Criteria ◽  
Spline Collocation ◽  
The Stability

Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integro differential equation (VIDE) by polynomial spline functions. The polynomial spline collocation method is stable if all eigenvalues of a matrix are in the unit disk and all eigenvalues with|λ|=1belong to a1×1Jordan block. Also many other conditions are derived depending upon the choice of collocation parameters used in the solution procedure.

scholarly journals The stability of collocation methods for higher-order Volterra integro-differential equations

2005 ◽  
Vol 2005 (19) ◽  
pp. 3075-3089 ◽  
Author(s):  
Edris Rawashdeh ◽  
Dave McDowell ◽  
Leela Rakesh
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Numerical Stability ◽  
Polynomial Spline ◽  
Higher Order ◽  
Collocation Methods ◽  
New Method ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
The Stability

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the new method are given and the efficiency of the new method is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-order integro-differential equations.

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