STABILITY OF THE SPLINE COLLOCATION METHOD FOR SECOND ORDER VOLTERRA INTEGRO‐DIFFERENTIAL EQUATIONS

2004 ◽  
Vol 9 (1) ◽  
pp. 79-90 ◽  
Author(s):  
M. Tarang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Collocation Method ◽  
Numerical Stability ◽  
Second Order ◽  
Spline Collocation ◽  
Spline Collocation Method ◽  
Integro Differential Equation ◽  
Numerical Tests

Numerical stability of the spline collocation method for the 2nd order Volterra integro‐differential equation is investigated and connection between this theory and corresponding theory for the 1st order Volterra integro‐differential equation is established. Results of several numerical tests are presented. Straipsnyje nagrinejamas antros eiles Volteros integro‐diferencialiniu lygčiu splainu kolokaci‐jos metodo skaitinis stabilumas ir nustatytas ryšys tarp šios teorijos ir atitinkamos pirmos eiles Volterra integro‐diferencialiniu lygčiu teorijos. Pateikti keleto skaitiniu eksperimentu rezultatai.

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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