Iterated Defect Correction for the Solution of Singular Initial Value Problems
نویسندگان
چکیده
منابع مشابه
Acceleration Techniques for Singular Initial Value Problems
The acceleration technique known as Iterated Defect Correction (IDeC) for the numerical solution of singular initial value problems is investigated. IDeC based on the implicit Euler method performs satisfactorily and can thus be used for the eÆcient solution of singular boundary value problems with the shooting method. Higher order one-step methods like the box scheme or the trapezoidal rule ca...
متن کاملReproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem
In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agr...
متن کاملNew Variants of Defect Correction for Boundary Value Problems in Ordinary Differential Equations
In this paper we discuss new variants of the acceleration technique known as Iterated Defect Correction (IDeC) for the numerical solution of boundary value problems in ordinary differential equations. A first approximation, computed by the backward Euler scheme, is iteratively improved to obtain a high order solution. Typically, the maximal attainable accuracy is limited by the smoothness of th...
متن کاملAnalytical and numerical treatment of a singular initial value problem in avalanche modeling
We discuss a leading-edge model used in the computation of the run-out length of dry-flowing avalanches. The model has the form of a singular initial value problem for a scalar ordinary differential equation describing the avalanche dynamics. Existence, uniqueness and smoothness properties of the analytical solution are shown. We also prove the existence of a unique root of the solution. Moreov...
متن کاملSOLVING SINGULAR ODES IN UNBOUNDED DOMAINS WITH SINC-COLLOCATION METHOD
Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...
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:
- SIAM J. Numerical Analysis
دوره 38 شماره
صفحات -
تاریخ انتشار 2001