A road map of methods for approximating solutions of two-point boundary-value problems
My aim in this paper has been to explain briefly what each of a variety of methods is, how methods relate to one another, and where are the difficulties today that stimulate interesting research problems. To describe what the methods are and how they relate we viewed each method as a Solution Technique for some Discrete Model of a Transformed Problem. Those areas which in my opinion deserve much more study and development include: numerical effects and efficiency of different methods of solving the linear algebraic systems that arise; methods for solving the special nonlinear algebraic systems that arise; comparative performance of codes implementing various methods on carefully chosen classes of test problems; and methods for estimating and controlling global errors by automatic selection of parameters of the method.
KeywordsFinite Difference Discrete Model Richardson Extrapolation Linear Algebraic System Transform Problem
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