Variable-order, variable-step methods for second-order initial-value problems
A variable-order, variable-step algorithm for solving second-order initial value problems with oscillating solution is produced. This algorithm is based on second-, fourth-, sixth- and eighth-order P-stable methods developed by the authors previously. The methods are derived in order to satisfy the order and P-stability conditions. In this paper the emphasis is on the combination of second-, fourth-, sixth- and eighth-order P-stable methods in a variable-step, variable-order algorithm in such a way that computational efficiency can be obtained.
scientific article; zbMATH DE number 1022223