P-stable symmetric super-implicit methods for periodic initial value problems

Abstract. How complex could the solution be to an initial value problem given by a polynomial-time computable function? This question can be given a natural and precise sense in computational complexity theory. In this note, we put together several results stating that more conditions

A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type:

Plane viscous channel flows are perturbed and the ensuing initial-value problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this work offers a means whereby completely arbitrary initial input can be speci ed without having

Abstract: New scheme for solving initial value problem of ordinary differential equation was derived. Starting from the general method of deriving the spline function, the scheme was developed based on interpolation and collocation. Key words: Initial value problems, ordinary differential equations

On global error estimation and control for initial value problems

of symmetries of an initial-value problem (or boundary-value problem) is a subset of the set of symmetries of the differential equation. The current paper demonstrates that this is untrue; indeed, an initial-value problem may have no symmetries in common with the underlying differential equation. The paper also

We show, in answer to K. Ko’s question raised in 1983, that an initial value problem given by a polynomial-time computable, Lipschitz continuous function can have a polynomial-space complete solution.

Symmetric eigenvalue problem &

then it is convergent with an error of order O(h) for all sufficiently smooth problems. Thus, if we integrate from 0 to 1 with step h = 10−5, we will need to perform 105 function evaluations to complete the integration and obtain a solution with error O(h). To achieve extra accuracy using this method we could reduce