2. Taylor Series Method
The approximate numerical solution to the I.V.P. y’(t) = f(t,y) over [t0, tm] is derived by using formula (1) on each subinterval [tk, tk+1]. The general step for Taylor’s method of order N is
where dj = y(j)(tk) for j = 1, 2, . . . , N at each step k = 0, 1, . . . , M - 1.