Mathematical Physics - Volume II - Numerical Methods

Chapter 2. Finite element method

48

which gives us:

C ( U n + 1 − 2 U n + U n − 1 ) = ( − KU n + f n ) ∆ t 2 .

(2.116)

It is necessary to know U 0 and U 1 = U 0 + ∆ t ∂ U 0

2 from equation (2.116),

∂ t in order to calculate U

and then calculate U 3 base on U 1 and U 2 , . . . Thus, the solution is conditionally stable.