standing-o/heat_equation

Numerical solutions of heat equations

Heat Equation

• Fundamental numerical methods solving heat equations
• Activities in scientific computing lab
• Dec. 3, 2019

1. Explicit - Forward Difference

• alpha = dt/h^2 <= 0.5
• Calculate 'Nx' times -> O(N)
• First order accuracy in time, second order accuracy in space i.e o(dt)

2. Implicit - Backward Difference

• alpha <= inf
• Calculate 'Nx^2' times -> O(N^2)
• First order accuracy in time, second order accuracy in space i.e o(dt)

3. Crank - Nicolson (theta-method)

• alpha <= inf
• Calculate 'Nx^2 + Nx' times -> O(N^2 + N)
• Second order accuracy in time and space i.e o(dt^2)