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Chain Matrices and the Crank-Nicolson Equation

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1 Author(s)

In Reference 1, a practical application of the special properties of a class of matrices called chain matrices is made to obtain numerical solutions of partial differential equations of the elliptic type. In this communication, we wish to present an application of these matrices to the study of the problem of obtaining numerical solutions of parabolic partial differential equations. This method is not proposed as a general method for obtaining a numerical solution to parabolic equations, for its limitations are obvious. Its use, however, does allow us to obtain some interesting theoretical results

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

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IBM Journal of Research and Development  (Volume:9 ,  Issue: 3 )