Unformatted text preview: 9 Finite Diﬀerences 9.1 Introduction 9.2 Diﬀerence Representations of PDEs Problems
1. Utilize Taylor series expansions about the point (n + , j ) to determine the T.E. of the
Crank Nicolson representation of the heat equation. Compare these results with the T.E.
obtained from Taylor series expansion about the point (n, j ).
2. The DuFort Frankel method for solving the heat equation requires solution of the diﬀerence equation
un+1 − un−1
un+1 − un+1 − un−1 + un−1
Develop the stability requirements necessary for the solution of this equation. 303 ...
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- Fall '08
- Taylor Series, 1 j, Crank Nicolson, DuFort Frankel method, Crank Nicolson representation