Deriving an Arbitrary Predictor Corrector Method

For Solving Ordinary Differential Equations

Colin Mitchell

Beginning with

we can estimate f with a Lagrange Interpolating polynomial. Using points , we get

Substituting this into the differential equation, we get

If we let , we get

Now if we let , we get

So our predictor becomes

For the corrector, we want to integrate the differential equation over . We will approximate f again with a Lagrange Interpolating Polynomial, however we will use the points . We will then get

If we let , we get

Also, if we let , we get

So our differential equation becomes