Composition methods for differential equations with processing

Abstract. We construct numerical integrators for differential equations up to order 12 obtained by composition of basic integrators. The following cases are considered: (i) composition for a system separable in two solvable parts, (ii) composition using as basic methods a first-order integrator and its adjoint, (iii) composition using second-order symmetric methods, and (iv) composition using fourth-order symmetric methods. Each scheme is implemented with a processor or corrector to improve their efficiency, and this can be done virtually cost-free