WOLFRAM|DEMONSTRATIONS PROJECT

Two-Step and Four-Step Adams Predictor-Corrector Method

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Adams predictor-corrector
two-step
four-step
initial points
Euler
Runge-Kutta
relative error
solution
step size
0.1
Consider the initial value problem
y'(t)=f(t,y)=-
2
y
+t/(
2
t
+1)
, with
y(0)=1
. This Demonstration uses the two-step and four-step Adams predictor-corrector method to find the estimated solution
y
Adams,i
of this first-order ordinary differential equation. In addition, the relative error
E
is calculated for
N
selected values of
t
, where
E=(
y
Adams,i
-
y
NDSolve,i
)
y
NDSolve,i

(i.e., we compare Adams method's solution
y
Adams
with the result obtained using NDSolve,
y
NDSolve
). Finally, the Euclidean norm of the absolute error vector is given (i.e.,
ϵ=
N
∑
i=1
2

y
Adams,i
-
y
NDSolve,i

).