TY  - JOUR
ID  - Cash2006
LB  - Cash2006
AU  - Cash, Jeff R.
TI  - The numerical solution of nonlinear two-point boundary value problems using iterated deferred correction - a survey
ST  - The numerical solution of nonlinear two-point boundary value problems using iterated deferred correction - a survey
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 2
SP  - 269
EP  - 287
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.2.269
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.2.269
AB  - The use of iterated deferred correction has proved to be a very efficient approach to the numerical solution of general first order systems of nonlinear two-point boundary value problems. In particular the two high order codes TWPBVP.f, based on mono-implicit Runge-Kutta (MIRK) formulae, and TWPBVPL.f based on Lobatto Runge-Kutta formulae as well as the continuation codes ACDC.f and COLMOD.f are now widely used. In this survey we describe some of the problems involved in the derivation of efficient deferred correction schemes. In particular we consider the construction of high order methods which preserve the stability of the underlying formulae, the choice of the mesh choosing algorithm which is based both on local accuracy and conditioning, and the computation of continuous solutions.
KW  - deferred correction
KW  - boundary value problems
KW  - conditioning
KW  - mesh selection
SN  - 1232-9274
ER  -