1 / 16

Finite Difference Method

Finite Difference Method. Major: All 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.

stefanie
Download Presentation

Finite Difference Method

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Finite Difference Method Major: All 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

More Related