Finite-difference method for stationary PDEs : Problem position

Problem position
Finite-difference method for stationary PDEs

Author : Pierre SPITERI

Publication date: October 10, 2002 | Lire en français

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1. Problem position

Let Ω be any bounded domain of $ℝ^{2}$ and ¶ Ω its boundary. We propose to determine the solution u (x,y ) of the classical Poisson problem with homogeneous Dirichlet boundary conditions: ${\begin{matrix} - Δ u = f dans Ω \\ u = 0 sur \partial Ω \end{matrix}$

with :

...

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Problem discretization. Case of the one-dimensional problem

References

(1) - DAUTRAY (R.), LIONS (J.-L.) - Analyse mathématique et calcul numérique pour les sciences et les techniques. - Tome 1 à tome 9, Masson (1988).
(2) - FORSYTHE (G.), WASOV (W.) - Finite difference methods for partial differential equations. - Wiley...

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Problem position Finite-difference method for stationary PDEs

1. Problem position

References

Problem position
Finite-difference method for stationary PDEs