pythNon: A PSE for the Numerical Solution of Nonlinear Algebraic Equations

Nonlinear algebraic equations (NAEs) occur routinely in many scientific and engineering problems. The process of solving these NAEs involves many challenges, from finding a suitable initial guess to choosing an appropriate convergence criterion. In practice, Newton’s method is the most widely used robust, general-purpose method for solving systems of NAEs. Many variants of Newton’s method exist. However, it is generally impossible to know a priori which variant of Newton’s method will be effective for a given problem. Moreover, the user usually has little control over many aspects of a software library for solving NAEs. For example, the user may not be able to specify easily a particular linear system solver for the Newton direction. This paper describes a problemsolving environment (PSE) called pythNon for solving systems of NAEs. In pythNon, users have direct and convenient access to many aspects of the solution process not ordinarily available in publicly available numerical software libraries. Consequently, the framework provided by pythNon facilitates a much wider exploration of strategies for solving NAEs than is otherwise presently possible. We give some examples to show how pythNon can be used. c © 2008 European Society of Computational Methods in Sciences and Engineering