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Computational Mechanics 5 - Boundary Value Problems

01_Revisiting_derivatives

  • How to approximate error in approximate derivatives
  • How to approximate derivatives using forward difference methods
  • How to approximate derivatives using backward difference methods
  • How to approximate derivatives using central difference methods
  • How to approximate higher order derivatives with forward, backward, and
  • central differences

02_Keep_it_steady

  • The difference between a PDE and an ODE
  • How to approximate differential equations with boundary conditions
  • Solve steady-state heat transfer problem
  • Solve static deflection of elastic beam
  • Demonstrate convergence of finite difference solutions

03_Good_Vibrations

  • How to set up and solve an eigenvalue problem
  • How eigenvalues and eigenvectors relate to natural frequencies and mode shapes
  • How to turn a PDE into a finite difference ODE
  • How to use eigenvalues to calculate natural frequencies of a vibrating string
  • How to solve a coupled set of ODEs
  • Visualize solutions to finite difference equations with 3D plots and
  • animations
  • How to listen to vibration solutions
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