Extrapolation Methods in Mathematica

This article outlines design and implementation details of the framework for one step methods for solving ordinary differential equations in Mathematica. The solver breaks up the solution into three main phases for equation processing and classification, numerical solution and processing of results. One of the distinguishing features of the framework is the hierarchical nature of the method invocation which allows for simple construction of composed integration schemes. A plug-in facility for user defined schemes is also provided. Highly accurate reference solutions can also be obtained by making use of arbitrary precision software arithmetic. Issues relating to appropriate formulation and efficient implementation will also be discussed, together with strategies for automatic method, order and parameter selection.