Recursive form of Sobolev gradient method for ODEs on long intervals

@article{Mujeeb2008RecursiveFO,
title={Recursive form of Sobolev gradient method for ODEs on long intervals},
author={D. Mujeeb and J. W. Neuberger and Sultan Sial},
journal={Int. J. Comput. Math.},
year={2008},
volume={85},
pages={1727-1740}
}

The Sobolev gradient method has been shown to be effective at constructing finite-dimensional approximations to solutions of initial-value problems. Here we show that the efficiency of the algorithm as often used breaks down for long intervals. Efficiency is recovered by solving from left to right on subintervals of smaller length. The mathematical formulation for Sobolev gradients over non-uniform one-dimensional grids is given so that nodes can be added or removed as required for accuracy. A… CONTINUE READING