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Implementation issues in solving nonlinear equations for two-point boundary value problems. (English) Zbl 0721.65043

Complex numerical methods often contain subproblems that are easy to state in mathematical form, but difficult to translate into software. Several algorithmic issues of this nature arise in implementing a Newton iteration scheme as part of a finite-difference method for two-point boundary value problems. We describe the practical as well as theoretical considerations behind the decisions included in the final code, with special emphasis on two “watchdog” strategies designed to improve reliability and allow early termination of the Newton iterates.
Reviewer: J.R.Cash

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations

Software:

COLNEW; COLSYS; PASVA3
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References:

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