Higher order methods
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There are two principal means to derive higher order methods y n+1 = p j=0 a j y n−j + h p j=−1 b j f (x n−j , y n−j) (a) Method of Undetermined Coefficients (b) Numerical Integration UNDETERMINED COEFFICIENTS Pick p > 0 and m > 1. Solve the linear system p j=0 a j = 1 p j=0 (−1) i a j + i p j=−1 (−1) i−1 b j = 1 for i = 1, ..., m.