Numerical Treatment of a Fourth Order Parabolic Partial Differential Equation

@article{Crandall1954NumericalTO,
title={Numerical Treatment of a Fourth Order Parabolic Partial Differential Equation},
author={Stephen H. Crandall},
journal={J. ACM},
year={1954},
volume={1},
pages={111-118}
}

The problem considered in this paper is that of finding finite difference approximations to solutions of + ~2'6= 0 (1) ~x 4 ~t 2 which satisfy prescribed initial conditions for ~b and~/~t in 0<x<l at t = 0 and which satisfy prescribed boundary conditions for ~b and ~/~x at x = 0 and x = 1 for subsequent t. This formulation represents (in dimensionless terms) the problem of predicting the transient response of a uniform flexible beam clamped at both ends, whose displacements and velocities are… CONTINUE READING