Week 5 - Mid term project -Stability analysis in the unsteady problem

Stability Analysis:

An important criterion which indicates at the stability of an equation is the Courant Friedrichs Lewy Condition or CFL condition which determines conditions necessary for convergence while solving certain partial differential equations numerically by finite differences methods.

Explicit Method:

Unstable solution graph:

In my case

alpha=1e-4

dt=1.01

CFL_number=0.2525

The solution is unstable

Implicit Form:

Implicit form is stable for large values of dt and the value of C ie CFL number does not affect the stabilty of the solution.

Implicit Schemes time accuracy decreases with increase in time steps.

Implicit Schemes are unconditionally stable and it uses entire domain to calculate each time steps therefore not affected by the CFL number.