Introduction to Scientific Computing - Tutorial 13: Recapitulation

Linear multi-step methods
k∑
k∑
α j x n+j = h β j f n+j , α k = 1, |α 0 | + |β 0 | ≠ 0
j=0
j=0
where f n+j = f (t n+j , x n+j ).
Euler’s explicit method:
x n+1 = x n + hf (t n , x n )
Euler’s implicit method:
x n+1 = x n + hf (t n+1 , x n+1 )
1. Februar 2013 Bojana Rosic Introduction to Scientific Computing Seite 14