An extended Crank-Nicholson method and its applications in the solution of partial differential equations: 1-D and 3-D conduction equations

Authors:
Nikos E. Mastorakis
Affiliations:
WSEAS, Research and Development Department, Agiou Ioannou, Theologou, Zografou, Athens, Greece and Military Institutes of University Education (ASEI), Hellenic Naval Academy, Piraeus, Greece
Venue:
MATH'06 Proceedings of the 10th WSEAS International Conference on APPLIED MATHEMATICS
Year:
2006

Citing 1
Cited 2

On the solution of ill-conditioned systems of linear and non-linear equations via genetic algorithms (GAs) and Nelder-Mead simplex search

EC'05 Proceedings of the 6th WSEAS international conference on Evolutionary computing

Electromagnetic and thermal model parameters of oil-filled transformers

WSEAS Transactions on Circuits and Systems
Application of MATLAB: based solar dryer for cocoa drying

ACACOS'12 Proceedings of the 11th WSEAS international conference on Applied Computer and Applied Computational Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, an extention of the Crank-Nicholson method for solving parabolic equations is launched. The method uses finite differences. For the derivative of the variable of time, we use central difference at 4 points (instead of 2 points of the classical Crank-Nicholson method), while for the second-order derivatives of the other spatial variables we use lagrangian interpolation at 4 points of the central differences at 5 points (instead of lagrangian interpolation at 2 points of the central differences at 3 points of the classical Crank-Nicholson method). The method is illustrated below.