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6 - Boundary value problems

Published online by Cambridge University Press:  05 June 2012

Kenneth J. Beers
Affiliation:
Massachusetts Institute of Technology
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Summary

Boundary value problems (BVPs) involve the solution of ODEs or partial differential equations (PDEs) on a spatial domain, subject to boundary conditions that hold on the domain boundary. Many problems from solid and fluid mechanics, electromagnetics, and heat and mass transfer are expressed naturally as BVPs. The forms of these differential equations often resemble each other because they arise from similar conservation principles. Here the emphasis is upon BVPs that arise from problems in transport phenomena.

This chapter focuses upon real-space methods, in which a computational grid is overlaid upon the domain. The BVP is then converted into a set of ODEs for a time-dependent problem or a set of algebraic equations for a steady problem. This technique can be used even when no analytical solution exists, and can be extended to BVPs with multiple equations or complex domain geometries. Here, the focus is upon the methods of finite differences, finite volumes, and finite elements. These methods have many characteristics in common; therefore, particular attention is paid to the finite difference method, as it is the easiest to code. The finite volume and finite element methods also are discussed; however, as the reader is most likely to use these in the context of prewritten software, the emphasis is upon conceptual understanding as opposed to implementation.

Type
Chapter
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Numerical Methods for Chemical Engineering
Applications in MATLAB
, pp. 258 - 316
Publisher: Cambridge University Press
Print publication year: 2006

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  • Boundary value problems
  • Kenneth J. Beers, Massachusetts Institute of Technology
  • Book: Numerical Methods for Chemical Engineering
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812194.007
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  • Boundary value problems
  • Kenneth J. Beers, Massachusetts Institute of Technology
  • Book: Numerical Methods for Chemical Engineering
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812194.007
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Boundary value problems
  • Kenneth J. Beers, Massachusetts Institute of Technology
  • Book: Numerical Methods for Chemical Engineering
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511812194.007
Available formats
×