Convergence of one-leg methods for neutral delay integro-differential equations

摘要

The error analysis of one-leg methods for a class of nonlinear neutral delay integrodifferential equations (NDIDEs) is given. It is proved that an A-stable one-leg method with an appropriate quadrature rule applied to NDIDEs is convergent of order at least min{p,q + 1/2 } if the one-leg method is consistent of order p <= 2 in the classical sense for ODEs and the error order of the quadrature rule is O(h(q+1)). Numerical examples further confirm the theoretical results. (C) 2016 Elsevier B.V. All rights reserved.