Unformatted text preview: ,k ) ( δy ) 2 + O (( δx ) 2 )+ O (( δy ) 2 ) (5) Approximate u ( j,k ) by w ( j,k ) which satisﬁes: w ( j,k + 1)-2 w ( j,k ) + w ( j,k-1) ( δx ) 2 + w ( j + 1 ,k )-2 w ( j,k ) + w ( j-1 ,k ) ( δy ) 2 = f ( j,k ) (6) When δx = δy = h , this becomes 4 w ( j,k )-w ( j,k + 1)-w ( j,k-1)-w ( j + 1 ,k )-w ( j-1 ,k ) =-h 2 f ( j,k ) (7) For the points near the boundaries, 1 or 2 of the values on the LHS of (7) are known. 1...
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- Winter '08
- Numerical Analysis, Green's function, Laplace operator, Laplace's equation, Poisson's equation, Dirichlet boundary conditions, matrix storage convention