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Finite Difference Method

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

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Finite Difference Method

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

  2. Finite Difference Methodhttp://numericalmethods.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 http://numericalmethods.eng.usf.edu

  4. 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 of inner radius a and outer radius b, the 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, http://numericalmethods.eng.usf.edu

  5. Solution At node Step 1 Step 2 At node Step 3 At node http://numericalmethods.eng.usf.edu

  6. Solution Cont Step 4 At node Step 5 At node Step 6 At node http://numericalmethods.eng.usf.edu

  7. Solving system of equations http://numericalmethods.eng.usf.edu

  8. Solution Cont http://numericalmethods.eng.usf.edu

  9. Solution Cont Using the approximation of and Gives you http://numericalmethods.eng.usf.edu

  10. Solution Cont Step 1 At node Step 2 At node Step 3 At node http://numericalmethods.eng.usf.edu

  11. Solution Cont Step 4 At node Step 5 At node Step 6 At node http://numericalmethods.eng.usf.edu

  12. Solving system of equations http://numericalmethods.eng.usf.edu

  13. Solution Cont http://numericalmethods.eng.usf.edu

  14. Comparison of radial displacements Table 1 Comparisons of radial displacements from two methods http://numericalmethods.eng.usf.edu

  15. Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit http://numericalmethods.eng.usf.edu/topics/finite_difference_method.html

  16. THE END http://numericalmethods.eng.usf.edu

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