An Efficient Asymptotically Correct Error Estimator for Collocation Solutions to Singular Index-1 DAEs
نویسندگان
چکیده
A computationally efficient a posteriori error estimator is introduced and analyzed for collocation solutions to linear index-1 differential-algebraic equations with properly stated leading term exhibiting a singularity of the first kind. The procedure is based on a modified defect correction principle, extending an established technique from the context of ordinary differential equations to the differential-algebraic case. Using recent convergence results for collocation methods, we prove that the resulting error estimate is asymptotically correct. Numerical examples demonstrate the performance of this approach. To keep the presentation reasonably selfcontained, some arguments from the literature on differential-algebraic equations concerning the decoupling of the problem and its discretization, which is essential for our analysis, are also briefly reviewed. The appendix contains a remark about the interrelation between collocation and implicit Runge-Kutta methods for differential-algebraic equations.
منابع مشابه
Defect-based A-posteriori Error Estimation for Index-1 DAEs
A computationally efficient a posteriori error estimator is introduced and analyzed for collocation solutions to linear index-1 DAEs with properly stated leading term. The procedure is based on a modified defect correction principle, extending an established technique from the ODE context to the DAE case. We prove that the resulting error estimate is asymptotically correct, and illustrate the m...
متن کاملConvergence of Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point
We analyze the convergence behavior of collocation schemes applied to approximate solutions of BVPs in nonlinear index 1 DAEs, which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity in the inherent nonlinear ODE system. In particular, we focus on the case when the inherent ODE system is singular with a singularity of the first kind and apply p...
متن کاملCollocation methods for index 1 DAEs with a singularity of the first kind
We study the convergence behavior of collocation schemes applied to approximate solutions of BVPs in linear index 1 DAEs which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity within the inherent ODE system. We focus our attention on the case when the inherent ODE system is singular with a singularity of the first kind, apply polynomial colloc...
متن کاملThe method of normal splines for linear DAEs on the number semi-axis
The method of normal spline-collocation (NSC), applicable to a wide class of ordinary linear singular differential and integral equations, is specified for the boundary value problems for differential-algebraic equations of second order on the number semiaxis. The method consists in minimization of a norm of the collocation systems’ solutions in an appropriate Hilbert–Sobolev space. The NSC met...
متن کاملPeriodic Solutions of Differential Algebraic Equations with Time Delays: Computation and Stability Analysis
This paper concerns the computation and local stability analysis of periodic solutions to semi-explicit differential algebraic equations with time delays (delay DAEs) of index 1 and index 2. By presenting different formulations of delay DAEs, we motivate our choice of a direct treatment of these equations. Periodic solutions are computed by solving a periodic two-point boundary value problem, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010