SIAM Journal on Scientific and Statistical Computing
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Runge-Kutta Software with Defect Control four Boundary Value ODEs
SIAM Journal on Scientific Computing
A new mesh selection strategy for ODEs
Applied Numerical Mathematics
A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
SIAM Journal on Matrix Analysis and Applications
Numerical approximation of nonlinear BVPs by means of BVMs
Applied Numerical Mathematics
COLSYS - - A Collocation Code for Boundary - Value Problems
Proceedings of a Working Conference on Codes for Boundary-Value Problems in Ordinary Differential Equations
International Journal of Computing Science and Mathematics
py_bvp: a universal Python interface for BVP codes
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
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We present a hybrid mesh selection strategy for use in codes for the numerical solution of two-point boundary value problems. This new mesh strategy is based on the estimation of two parameters which characterise the conditioning of the continuous problem as well as on a standard estimate of the local discretisation error. We have implemented this algorithm in the well known code TWPBVP and have found that the modified code is often considerably more efficient than the original. Another strong advantage of using the new mesh selection algorithm is that it automatically provides an estimate of the conditioning of the discrete problem. This is very valuable (arguably indispensible) for use either in an a posteriori error estimate or, in situations where the conditioning constants are large, as a warning that the accuracy obtained in the solution may be worse than anticipated.