Numerical solution of the one-dimensional Burgers’ equation: Implicit and fully implicit exponential finite difference methods

Pramana ◽  
2013 ◽  
Vol 81 (4) ◽  
pp. 547-556 ◽  
Author(s):  
BILGE INAN ◽  
AHMET REFIK BAHADIR
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Burgers Equation ◽  
Finite Difference Methods ◽  
One Dimensional ◽  
Fully Implicit ◽  
Difference Methods ◽  
The One

A method for the numerical integration of the one-dimensional heat equation using chebyshev series

1961 ◽  
Vol 57 (4) ◽  
pp. 823-832 ◽  
Author(s):  
David Elliott
Keyword(s):  
Finite Difference ◽  
Heat Equation ◽  
Finite Difference Methods ◽  
Linear Boundary ◽  
Chebyshev Series ◽  
One Dimensional ◽  
Difference Methods ◽  
The One ◽  
Image Position ◽  
General Linear Boundary Conditions

ABSTRACTA numerical solution ofwith general linear boundary conditions alongx= ±1, is described where at any timetthe Chebyshev expansion of θ(x,t) in –1 ≤x≤ 1 is computed directly. Compared with the more usual finite difference methods, this method requires much less computation and there are no stability problems. Two cases are considered in detail.

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