Two-Step and Four-Step Adams Predictor-Corrector Method
Two-Step and Four-Step Adams Predictor-Corrector Method
Consider the initial value problem , with . This Demonstration uses the two-step and four-step Adams predictor-corrector method to find the estimated solution of this first-order ordinary differential equation. In addition, the relative error is calculated for selected values of , where (i.e., we compare Adams method's solution with the result obtained using NDSolve, ). Finally, the Euclidean norm of the absolute error vector is given (i.e., ).
y'(t)=f(t,y)=-+t/(+1)
2
y
2
t
y(0)=1
y
Adams,i
E
N
t
E=(-)
y
Adams,i
y
NDSolve,i
y
NDSolve,i
y
Adams
y
NDSolve
ϵ=
N
∑
i=1
2
-
y
Adams,i
y
NDSolve,i