On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems

On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems

The convergence of shooting methods for singular boundary value problems

We investigate the convergence properties of single and multiple shooting when applied to singular boundary value problems. Particular attention is paid to the well-posedness of the process. It is shown that boundary value problems can be solved efficiently when a high order integrator for the associated singular initial value problems is available. Moreover, convergence results for a perturbed...

Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems

In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...

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...

On the convergence of finite difference methods for weakly regular singular boundary value problems

The second order finite difference methods M1 based on a non-uniform mesh and M2 based on an uniform mesh developed by Chawla andKatti [Finite differencemethods and their convergence for a class of singular two point boundary value problems, Numer. Math. 39 (1982) 341–350] for weakly regular singular boundary value problems (p(x)y′)′ = f (x, y), 0<x 1, with p(x)= xb0 , 0 b0< 1, and boundary con...