Explicit finite-difference methods for non-linear dynamic systems: Froude's pendulum

1996 ◽  
Vol 135 (3-4) ◽  
pp. 243-264 ◽  
Author(s):  
K. Djidjeli ◽  
Z. Guan ◽  
W.G. Price ◽  
E.H. Twizell
Keyword(s):  
Finite Difference ◽  
Dynamic Systems ◽  
Finite Difference Methods ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Non Linear ◽  
Difference Methods ◽  
Explicit Finite Difference

On the Solution of the Diffusion Equations by Numerical Methods

1966 ◽  
Vol 88 (4) ◽  
pp. 421-427 ◽  
Author(s):  
H. Z. Barakat ◽  
J. A. Clark
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Present Method ◽  
Finite Difference Methods ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Procedure ◽  
Implicit Methods ◽  
Difference Methods ◽  
Explicit Finite Difference

An explicit-finite difference approximation procedure which is unconditionally stable for the solution of the general multidimensional, nonhomogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment. Also it has the simplicity of the explicit methods and employs the same “marching” type technique of solution. Results obtained by this method for several different problems are compared with the exact solution and with those obtained by other finite-difference methods. For the examples solved the numerical results obtained by the present method are in closer agreement with the exact solution than are those obtained by the other methods.

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