ME 540

Numerical Solutions Applied To Heat Transfer And Fluid Mechanics Problems

Direct Solution Methods


Matrix inversion

For the implicit set of equations

The inverted or "explicit" set of equations is




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

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