SOME NEW FINITE-DIFFERENCE SCHEMES FOR PARABOLIC DIFFERENTIAL EQUATIONS
- 1 April 1982
- journal article
- research article
- Published by Taylor & Francis in Numerical Heat Transfer
- Vol. 5 (2) , 199-210
- https://doi.org/10.1080/10407788208913443
Abstract
Finite-difference schemes for parabolic differential equations are considered. It is well known that the Crank-Nicolson scheme can lead to considerable inaccuracy if the time step is large or the initial-value function is unfavorable. Methods that overcome these defects are known but, computationally, are considerably more expensive. Two families of schemes are presented here which also overcome these deficiencies in the Crank-Nicolson scheme but which involve no extra amount of computation.Keywords
This publication has 2 references indexed in Scilit:
- High-Accuracy Stable Difference Schemes for Well-Posed Initial-Value ProblemsSIAM Journal on Numerical Analysis, 1979
- A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction typeMathematical Proceedings of the Cambridge Philosophical Society, 1947