A New Class of Highly Accurate Solvers for Ordinary Differential Equations

We introduce a new class of numerical schemes for the solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs). Our algorithms are of the predictor-corrector type; they are obtained via the decomposition of the solutions of the ODEs into combinations of appropriately chosen exponentials, whereas the classical schemes are based on the approximation of solutions by polynomials. The resulting schemes have the advantage of significantly faster convergence, given fixed lengths of predictor and corrector vectors. The performance of the approach is illustrated via a number of numerical examples. A new class of highly accurate solvers for ordinary differential equations