A new class of highly accurate solvers for ordinary differential equations

his talk will describe a new class of numerical schemes for the solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs). The 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, where the classical schemes are
based on the approximation of solutions by polynomials. The resulting schemes have the advantage of significantly faster
convergence.
The performance of the approach is illustrated via a number of
numerical examples.

The results presented in this talk are joint work with Vladimir Rokhlin and are part of the speaker’s dissertation.