A parallel DIRK method for stiff initial-value problems

An automatic multistep method for solving stiff initial value problems

A multistep method with matricial coefficients is developed. It can be used to solve stiff initial value problems of the form y’= Ay + g(x,y). This method bears the nature of the classical Adams-Bashforth-Moulton PC formula and can be shown to be consistent, convergent and A-stable. A careful reformulation of this method legitimatizes the implementation of this algorithm in a variable-step vari...

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.

Parallel Implementation of a Validated Method for Initial Value Problems

Neumaier’s Method for the Solution of Initial Value Problems for Stiff Ordinary Differential Equations

Neumaier’s Method For The Solution Of Initial Value Problems For Stiff Ordinary Differential Equations Annie Hsiao Chen Yuk Master of Science Graduate Department of Computer Science University of Toronto 2005 Compared with standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs), validated methods not only compute a numerical solution to a problem,...

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...