A New Class Of Highly Accurate Solvers For Ordinary Differential Equations

摘要

We introduce a new class of predictor-corrector schemes for the numerical solution of the Cauchy problem for non-stiff ordinary differential equations (ODEs), obtained via the decomposition of the solutions into combinations of appropriately chosen exponentials; historically, such techniques have been known as exponentially fitted methods. The proposed algorithms differ from the classical ones both in the selection of exponentials and in the design of the quadrature formulae used by the predictor-corrector process. 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.