A perturbed collocation method for boundary-value problems in differential-algebraic equations

摘要

This paper introduces a perturbed collocation method for linear boundary-value problems (BVP) in differential-algebraic equations (DAE) with index one. In contrast with the usually direct approximation of the collocation method for ordinary differential equations (ODE) to BVPs in DAEs, the proposed method is stable and preserves superconvergence. Numerical experiments confirm the results.