Department of Mathematics
Collocation methods for general volterra functional integral equations with vanishing delays
We analyze the existence, uniqueness, and regularity properties of solutions for general Volterra functional integral equations with the delay function θ(t) vanishing at the initial point of the given interval [0, T] (with θ(t) = qt, 0 > q > 1, representing an important special case). The focus of the paper is then on the the attainable order of convergence, and the question of possible superconvergence, for collocation solutions in certain piecewise polynomial spaces. Numerical experiments complement the theoretical convergence results. © 2011 Society for Industrial and Applied Mathematics.
Collocation solutions, Existence and regularity of solutions, Optimal order of convergence, Pantograph-type delays, Vanishing delays, Volterra functional integral equations
Source Publication Title
SIAM Journal on Scientific Computing
Society for Industrial and Applied Mathematics
Xie, Hehu, Ran Zhang, and Hermann Brunner. "Collocation methods for general volterra functional integral equations with vanishing delays." SIAM Journal on Scientific Computing 33.6 (2011): 3303-3332.