Uniform L-1 error bounds for the semidiscrete solution of a volterra equation with completely monotonic convolution kernel
We study the second-order continuous time Galerkin approximation of the solution ut + J(0)(t) beta(t - delta) Au(s) ds = 0, u(0) = v, t > 0, where A is an elliptic partial-differential operator and,0(t) is completely monotonic and locally integrable, but not constant. Error estimates are derived in the norm of L-t(1) (0, infinity L-x(2)). (C) 2002 Elsevier Science Ltd. All rights reserved.
volterra equation completely monotonic kernel finite element uniform error bound