PARAEXP: A Parallel Integrator for Linear Initial-Value Problems

PARAEXP: A Parallel Integrator for Linear Initial-Value Problems

A novel parallel algorithm for the integration of linear initial-value problems is proposed. This algorithm is based on the simple observation that homogeneous problems can typically be integrated much faster than inhomogeneous problems. An overlapping time-domain decomposition is utilized to obtain decoupled inhomogeneous and homogeneous subproblems, and a near-optimal Krylov method is used fo...

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...

Parallel Implementation of a Validated Method for Initial Value Problems

MODIFIED K-STEP METHOD FOR SOLVING FUZZY INITIAL VALUE PROBLEMS

We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia