Direct reductions of partial differential equations to systems of ordinary differential equations are in one-to-one correspondence with compatible differential constraints. The dif...
An explicit time-stepping method is developed for adaptive solution of time-dependent partial differential equations with first order derivatives. The space is partitioned into bl...
In this paper, we give a necessary and sufficient condition for an algebraic ODE to have an algebraic general solution. For an autonomous first order ODE, we give an optimized bo...
We propose algorithms for the computation of the first N terms of a vector (or a full basis) of power series solutions of a linear system of differential equations at an ordinary ...
In the past few years, there has been a trend of providing increased computing power through greater number of cores on a chip, rather than through higher clock speeds. In order t...