AN IMPLICIT, NUMERICAL METHOD FOR SOLVING THE TWO-DIMENSIONAL HEAT EQUATION
A generalization of the one-dimensional Peaceman and Rachford method is derived. ln this generalization simuitaneous cquations are set up and solved once for all values of the temperature over the entire twodimensional mesh. This method is extended to treat nonlinear heat flow and it is unconditionally stable. both for linear and nonlinear problems. In the nonlinear case an iterative scheme is employed to solve the simultaneous equations which provides second- order convergence. This method differs from the well-known alternating-direction method in that the alternatingdirection method does not solve the complete set of simultaneous equations at each time step, but only a one-dimensional facsimile of them, and its range of applicability is more restricted. (auth)
- Research Organization:
- Los Alamos Scientific Lab., N. Mex.
- DOE Contract Number:
- W-7405-ENG-36
- NSA Number:
- NSA-13-000797
- OSTI ID:
- 4295233
- Report Number(s):
- LA-2232
- Country of Publication:
- United States
- Language:
- English
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