High order numerical integrators for differential equations using composition and processing of low order methods Original Research Article

In this paper we build high order integrators for solving ordinary differential equations by composition of low order methods and using the processing technique. From a basic pth-order method, View the MathML source, one can obtain high order integrators in the processed form View the MathML source (n>p) being both the processor, View the MathML source, and the kernel, View the MathML source, compositions of the basic method. The number of conditions for the kernel is drastically reduced if we compare with a standard composition. The particular case in which View the MathML source is a symmetric scheme of order 2 and 4, respectively, is analyzed, and new optimized 4th-, 6th- and 8th-order integrators are built.