Parallel algorithms for initial-value problems for difference and differential equations
Journal of Computational and Applied Mathematics
On Testing a Subroutine for the Numerical Integration of Ordinary Differential Equations
Journal of the ACM (JACM)
Parallel multiple shooting for the solution of initial value problems
Parallel Computing
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In this paper we propose a parallel implementation of one-step methods with stepsize control for the numerical solution of IVPs for ODEs of the form y'(t)=f(t, y(t)), y(t"0)=y"0. The proposed implementation is based on the fact that any one-step ODE-method on a mesh {t"0"n), y"0 known. In a previous paper (1989) we introduced a paral iterative algorithm for the approximation of the trajectory (y"0, y"1,..., y"N), in which a block of guessed values (u^0"0 := y"0, u^0"1,..., u^0"N is iterated, concurrently with respect to the index n, until an error proportional to a given iteration tolerance TOL "i"t is reached. Here that parallel algorithm is developed further in order to perform the stepsize control strategy, according to a given step tolerance TOL "s"t. Moreover, an analysis of the optimal ratio between TOL "i"t and TOL "s"t is given. The paper ends with numerical examples and estimations of the attainable speedup.