Remarks on the choice of a stiff ordinary differential equation solver

A Highly Accurate Solver for Stiff Ordinary Differential Equations

We introduce a solver for stiff ordinary differential equations (ODEs) that is based on the deferred correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadra...

We a Highly Accurate Solver for Stiff Ordinary Differential Equations

correction scheme for the corresponding Picard integral equation. Our solver relies on the assumption that the solution can be accurately represented by a combination of carefully selected complex exponentials. The solver’s accuracy and stability rely on the computation of highly accurate quadrature weights for the integration of the selected exponentials on equidistant nodes. We analyze our so...

A Universal Ordinary Differential Equation

An astonishing fact was established by Lee A. Rubel in 81: there exists a fixed non-trivial fourthorder polynomial differential algebraic equation (DAE) such that for any positive continuous function φ on the reals, and for any positive continuous function (t), it has a C∞ solution with |y(t) − φ(t)| < (t) for all t. Lee A. Rubel provided an explicit example of such a polynomial DAE. Other exam...

A Parallel Algorithm for Stiff Ordinary Differential Equations

The problem associated with the stiff ordinary differential equation (ODE) systems in parallel processing is that the calculus can not be started simultaneously on many processors with an explicit formula. The proposed algorithm is constructed for a special classes of stiff ODE, those of the form y'(t)=A(t)y(t)+g(t). It has a high efficiency in the implementation on a distributed memory multipr...

A quasi-interpolation method for solving stiff ordinary differential equations