l5 - Lecture 5: Overview of Numerical Methods (contd) 1...

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Lecture 5: Overview of Numerical Methods (cont’d) 1
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Last time… Examined important classes of partial differential equations and understood their behavior Saw how this knowledge would apply to the general scalar transport equation Started an overview of numerical methods including mesh terminology, finite difference, finite volume and finite element methods 2
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This time… We will continue the overview and examine Accuracy, consistency, stability and convergence of a numerical scheme 3
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Solution of Linear Equations Linear equation set has two important characteristics » Matrix is sparse, may be banded » Coefficients are provisional for non-linear problems Two different approaches » Direct methods » Iterative methods Approach defines “path to solution” » Final answer only determined by discretization 4
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All discretization schemes lead to Here is solution vector [ 1 , 2 ,…, N ] T . Can invert : Inversion is O(N 3 ) operation. Other more efficient methods exist. » Take advantage of band structure if it exists
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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l5 - Lecture 5: Overview of Numerical Methods (contd) 1...

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