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 integro-differential 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+12}, 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(hq+1). Numerical examples further confirm the theoretical results.