A Highly Accurate Solver for Stiff Ordinary Differential Equations

Abstract

We introduce a solver for stiff ordinary differential equations 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 quadrature weights for the integration of the selected exponentials on equidistant nodes. We analyze our solver stability and accuracy regions, and demonstrate its fast convergence on stiff problems. The solver is combined with an adaptive step-size scheme employing interpolation formulas for the exponentially fitted solution.