Computational Mechanics 5 - Boundary Value Problems#
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
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
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