Optimality of theoretical error estimates for spline collocation methods for linear weakly singular Volterra integro-differential equations

2005 ◽  
Vol 54 (3) ◽  
pp. 162
Author(s):  
I Parts
Keyword(s):  
Differential Equations ◽  
Error Estimates ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Theoretical Error ◽  
Weakly Singular

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.

scholarly journals Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Feras M. Al Faqih
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Error Estimates ◽  
Closed Contour ◽  
Lebesgue Spaces ◽  
Solvability Conditions ◽  
Mechanical Quadrature ◽  
Weakly Singular ◽  
Quadrature Methods ◽  
Singular Integrodifferential Equations

The present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. The equations are defined on an arbitrary smooth closed contour of the complex plane. Error estimates and convergence for the investigated methods are established in Lebesgue spaces.

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