Quantitative Methods: Numerical Solution of DEs

[symsane]

Homework Statement

Show that if we fit f(x) over [xn,xn+1], with a first-degree polynomial that interpolates f at xn and xn+1, then f(x)=f(xn)+[f(xn+1)-f(xn)](x-xn)/h. Putting that approximation into the relevant equation 1 which is given at relevant equations part derive the approximation:
y(xn+1)=y(xn)+1/2[f(xn)+f(xn+1)]h

Homework Equations

eq.1 : y(xn+1) = y(xn) + f(xn+1) - f(xn)

Also we know that y'=f(x) and y(xn+1)=y(xn)+f(xn)h

 

[Mark44]

What have you done? If you haven't done so, draw a picture. Your interpolation polynomial is first-degree, which means it's a straight line.