ME 540

Numerical Solutions Applied To Heat Transfer And Fluid Mechanics Problems


Direct Solution Methods

Characteristics



Matrix inversion

For the implicit set of equations

The inverted or "explicit" set of equations is



EXAMPLE



IMPLICIT





EXPLICIT





Progressive Elimination

See a discussion extracted from CmpSci 201F notes for a discussion of the details of Gaussian elimination and LU factorization. We can use the efficiencies associated with factorization to cut the level of roundoff error in a given direct solution. However, you should understand that matrices exist for which roundoff can not be controlled within a standard LU factorization (even with pivoting). When the off-diagonal coefficients




Other Lectures / Home


Created by Frank Schmidt
Maintained by John Mahaffy : jhm@psu.edu