Suggestions for Real-World Applications of System of Linear Equations/Numerical Integration

NOTE

I haven’t read the papers in great detail and just skimmed the abstract. They may be unrelated to our lesson, or may be significantly more advanced.

System of Linear Equations (Gauss-Jordan Elimination, LU Decomposition, and etc.)

• Applications
  • Simple models for rocket, pressure vessel, and trunnion
  • RLC Circuits
  • Hospitals: data envelopment analysis
  • Security, authentication scheme
  • Mobile application development
  • Software solution development
  • Traffic management
  • image authentication
  • balancing chemical equations
  • nuclear fuel depletion systems
  • Cholesky Decomposition (A modified version of LU Decomposition)
    • analysis of lightning
    • nuclear-electronic orbital theory
    • electronic-structure theory

Numerical Integration

• Applications
  • structure analysis (stiffness method)
    • helpful background info:
      • stiffness methods
  • floating structure analysis
    • related to floating on water
  • outcome prediction of an uncertain event
  • analysis of thin layer elements
    • helpful background info:
      • interface element
      • finite element analysis
  • population modeling that satisfy conservation laws
  • milling stability analysis
    • related with manufacturing
  • fluid flow
  • fluid dynamics
  • Simple models for rocket, product probabilities, and trunnion
  • robotics