The stability of collocation methods for VIDEs of second order

Edris  Rawashdeh; Dave  McDowell; Leela  Rakesh

doi:10.1155/IJMMS.2005.1049

International Journal of Mathematics and Mathematical Sciences (Jan 2005)

The stability of collocation methods for VIDEs of second order

Edris Rawashdeh,
Dave McDowell,
Leela Rakesh

Affiliations

Edris Rawashdeh: Department of Mathematics, Center for Applied Mathematics and Polymer Fluid Dynamics, Central Michigan University, Mount Pleasant 48859, MI, USA
Dave McDowell: Department of Mathematics, Center for Applied Mathematics and Polymer Fluid Dynamics, Central Michigan University, Mount Pleasant 48859, MI, USA
Leela Rakesh: Department of Mathematics, Center for Applied Mathematics and Polymer Fluid Dynamics, Central Michigan University, Mount Pleasant 48859, MI, USA

DOI: https://doi.org/10.1155/IJMMS.2005.1049
Journal volume & issue: Vol. 2005, no. 7
pp. 1049 – 1066

Abstract

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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|=1 belong to a 1×1 Jordan block. Also many other conditions are derived depending upon the choice of collocation parameters used in the solution procedure.

Published in International Journal of Mathematics and Mathematical Sciences

ISSN: 0161-1712 (Print); 1687-0425 (Online)
Publisher: Wiley
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://onlinelibrary.wiley.com/journal/6396

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