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## Finite Difference Methods

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### Title: Finite Difference Methods Author: Fritz Fiedler Last modified by: Fritz Fiedler Created Date: 1/20/2004 12:14:56 AM Document presentation format – PowerPoint PPT presentation

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Title: Finite Difference Methods

1
Finite Difference Methods
Definitions
2
Finite Difference Methods
Approximate derivatives
difference between exact derivative and its
approximation is the truncation error
3
Finite Difference Methods
Given a smooth function (i.e., a function that is
continuous and has continuous derivatives), the
Taylor series approximates the value of a
function at one point based on the value of the
function and its derivatives at another, nearby
point
4
Finite Difference Methods
First-order Taylor series
solving for the first derivative
5
Finite Difference Methods
Truncation error
6
Finite Difference Methods
Exercise write the Taylor series expansion for
q(x - Dx) and solve for the first differential...
7
Finite Difference Methods
Dx
t
Dt
n 1

n
n - 1
i
i - 1
i 1
x
8
Finite Difference Methods
Backward time difference explicit
Forward time difference implicit
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