Page 299 - Excel for Scientists and Engineers: Numerical Methods
P. 299
276 EXCEL: NUMERICAL METHODS
=C15+E15+C15
=D15+F15
=El 5+G15
=F15+H15+H15
Figure 12-8. A convenient spreadsheet layout for solving a parabolic PDE by
the Crank-Nicholson method. The coefficients matrix is aligned directly above
the table of values and the table of constants directly to the right.
(folder 'Chapter 12 (PDE) Examples, workbook 'Parabolic PDE', sheet 'Crank-Nicholson 1')
The set of simultaneous equations can be solved by methods described in
Chapter 9. In this case the solution was found by the matrix inversion method;
the array formula in cells D19:G19 is
{=MMULT(I 15: L15,MlNVERSE($D$S:$G$l 2)))
