Module 3: Higher order Single Step Methods
  Lecture 8: Higher Order Methods
 

 

Note: Since is not known, the RHS of (3.9) cannot be evaluated. Two approaches are possible. One is to attempt to solve the nonlinear equation (3.9) for . This is called an implicit method. Alternatively, one can estimate by another method, such as the Euler method, and get an explicit method. Then we get the formula

(3.10)