Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

1973 ◽  
Vol 12 (3) ◽  
pp. 349-353 ◽  
Author(s):  
J. LL. MORRIS ◽  
A. R. GOURLAY
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
One Dimensional

On the Crank-Nicolson procedure for solving parabolic partial differential equations

1957 ◽  
Vol 53 (2) ◽  
pp. 448-461 ◽  
Author(s):  
M. L. Juncosa ◽  
David Young
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Classical Problem ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Proof Of Convergence ◽  
Implicit Numerical Method ◽  
Crank Nicolson

ABSTRACTProof of convergence of the Crank-Nicolson procedure, an ‘implicit’ numerical method for solving parabolic partial differential equations, is given for the case of the classical ‘problem of limits’ for one-dimensional diffusion with zero boundary conditions. Orders of convergence are also given for different classes of initial functions. Results do not support the validity of so-called h2-extrapolation in some cases.

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