numerical analysis...

• Dec 16th 2008, 11:46 PM
greensoda119
numerical analysis...
Derive the Adams-Bashforth (AB) method for the following problem using the interpolationg polynomial of degree 2.( Explicit multi-step method )

Y'(x)=f(x,Y(x)) on x>0
Y(0)=Y lower case 0

Derive the Adams-Moulton (AM) method for the same problem using the interpolationg polynomial of degree 2.( Implicit multi-step method )

can anyone help me with this problem??
• Jan 14th 2011, 09:51 AM
lvleph
I know this is late, but what you want to do is setup the following
$\displaystyle y' = f(t,y) \Rightarrow \int_{t_k}^{t_{k+1}}\! y' \, dt = \int_{t_k}^{t_{k+1}}\! f(t,y) \, dt \Rightarrow y_{k+1} = y_k + \int_{t_k}^{t_{k+1}}\! f(t,y) \, dt$

For Adams-Bashforth interpolate $\displaystyle f(t,y)$ at the points $\displaystyle t_{k-2}, t_{k-1}, t_{k}$ using the Lagrange interpolating polynomial and then integrate.

For Adams-Moulton interpolate $\displaystyle f(t,y)$ at the points $\displaystyle t_{k-1}, t_k, t_{k+1}$ using the Lagrange interpolating polynomial and then integrate.