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## Finite Difference Method

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### Finite Difference Method. An example of a boundary value ordinary differential equation is ... Solving system of equations. http://numericalmethods.eng.usf.edu ... – PowerPoint PPT presentation

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Title: Finite Difference Method

1
Finite Difference Method
• Chemical Engineering Majors
• Authors Autar Kaw, Charlie Barker
• http//numericalmethods.eng.usf.edu
• Transforming Numerical Methods Education for STEM

2
Finite Difference Method http//numericalme
thods.eng.usf.edu
3
Finite Difference Method
An example of a boundary value ordinary
differential equation is
The derivatives in such ordinary differential
equation are substituted by finite divided
differences approximations, such as
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Example
Take the case of a pressure vessel that is being
tested in the laboratory to check its ability to
withstand pressure. For a thick pressure vessel
differential equation for the radial displacement
u of a point along the thickness is given by
The pressure vessel can be modeled as,
Substituting these approximations gives you,
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Solution
At node
Step 1
Step 2 At node
Step 3 At node
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Solution Cont
Step 4 At node
Step 5 At node
Step 6 At node
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Solving system of equations
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Solution Cont
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Solution Cont
Using the approximation of
and
Gives you
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Solution Cont
Step 1 At node
Step 2 At node
Step 3 At node
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Solution Cont
Step 4 At node
Step 5 At node
Step 6 At node
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Solving system of equations
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Solution Cont
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Table 1 Comparisons of radial displacements from
two methods
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