Differential Equations Lecture Work Solutions 303

Differential Equations Lecture Work Solutions 303 - 9...

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Unformatted text preview: 9 Finite Differences 9.1 Introduction 9.2 Difference Representations of PDEs Problems 1 1. Utilize Taylor series expansions about the point (n + , j ) to determine the T.E. of the 2 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 α j j = un+1 − un+1 − un−1 + un−1 j j j j 2∆t (∆x)2 Develop the stability requirements necessary for the solution of this equation. 303 ...
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