Adams' Method

Adams' method is a numerical method for solving linear first-order ordinary differential equations of the form

(1)

Let

(2)

be the step interval, and consider the Maclaurin series of about ,

(3)

(4)

Here, the derivatives of are given by the backward differences

			(5)
			(6)
			(7)

etc. Note that by (◇), is just the value of .

For first-order interpolation, the method proceeds by iterating the expression

(8)

where . The method can then be extended to arbitrary order using the finite difference integration formula from Beyer (1987)

(9)

to obtain

(10)

Note that von Kármán and Biot (1940) confusingly use the symbol normally used for forward differences to denote backward differences .