On sequential and parallel solution of initial value problems

On the randomized solution of initial value problems

Recently S. Heinrich and B. Milla presented an order optimal randomized algorithm solving this problem for γ-smooth input data (i.e. γ = r + ρ: the r-th derivatives of f satisfy a ρ-Hölder condition). This algorithm uses function values and values of derivatives of f . In this paper we present an order optimal randomized algorithm for the class of γ-smooth functions that uses only values of f ....

Parallel Solution of Elliptic Boundary Value Problems

We describe the development of some parallel iterative techniques for solving boundary value problems for elliptic partial differential equations. Using domain decomposition techniques, we modify standard sequential iterative techniques to obtain effective parallel methods. We contrast implementations on distributed-memory and shared-memory scalable parallel processors. We describe the use of t...

Parallel Methods for Initial Value Problems

As scientiic technology becomes increasingly more sophisticated, the production of more data and/or the modelling of more complex systems requires computers with ever-increasing computational power. In order to cope with this situation numerical algorithms have to be developed which allow the distribution of both data and code segments over large numbers of processors with the hope that problem...

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...

Numerical solution of fuzzy initial value problems under generalized dierentiability by HPM