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A comparative investigation on recurrence formulae in finite difference methods
Author(s) -
Haberland Christoph,
Lahrmann Andreas
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620250220
Subject(s) - padé approximant , mathematics , crank–nicolson method , thermal conduction , finite difference method , finite element method , backward euler method , euler's formula , mathematical analysis , finite difference , transient (computer programming) , time stepping , euler equations , discretization , physics , computer science , quantum mechanics , thermodynamics , operating system
To solve the transient heat‐conduction equation, the Pade‐approximation is introduced into the Finite Difference Method. But, if the time step is chosen too large relatively to the element size the Euler method (Pade (0,1) approximation) and the Crank–Nicolson solution (Pade (1,1)‐approximation) lead to significant oscillations. In contrast, the Full Implicit scheme (Pade (1,0)‐approximation) does not show this oscillatory behaviour, but is more inaccurate. Compared to these time stepping algorithms the presented Weighted Time Step method is seen to offer definite advantages.