floating point formula, error bound for rounding and chopping

Richardson extrpolation for trapezoidal

Simpson's proof

Peano's error formula

hw on simpson's

periodic function, rate of convergence

implement Richardson recursively.

cancelation and extra order of accuracy for integration

implement/apply Richardson extraplation analytically, then numerically.



Fact:

u''= f =  sin(\pi x), u(0)=u(1)=0

the solution can be obtained by the following
formula

u(1/2) = \int g(x,\xi) f(\xi) d \xi