# How i implement Adams Predictor-Corrector Method from general code ?

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Hazel Can on 25 May 2022
%------------------------------------------------------
% 2-step Predictor-Corrector
% [T,Y]=dd2(f,definition,y,h); definition=[t1,tfinal]
%------------------------------------------------------
function [T,Y]=dd2(f,definition,Y1,h)
t1=definition(1);tfinal=definition(2);T=t1;Y=Y1;
t2=t1+h;
definition=[t1,t2];
[T,Y]=rk2(f,definition,Y1,h) ;
Y2=Y(2);
while t2 <tfinal
t3=t2+h;
P=Y2+h*(3/2*f(t2,Y2)-1/2*f(t1,Y1));
Y3=Y2+h/12*(5* f(t3,P)+8*f(t2,Y2)-f(t1,Y1));
Y1=Y2; Y2=Y3;t1=t2;t2=t3;
T=[T;t3];Y=[Y;Y3];
end
%
%----------------------------------------------
##### 2 CommentsShowHide 1 older comment
Torsten on 27 May 2022
You know the correct result of your differential equation.
If you plot Y against T in the calling program and compare the plot with the analytical solution, both should be approximately the same.
If yes, your code is (most probably) correct, if not, it's not.

Lateef Adewale Kareem on 29 May 2022
Edited: Lateef Adewale Kareem on 30 May 2022
clc; clear all;
h = 0.01;
mu = 20;
f_m = @(t,y) mu*(y-cos(t))-sin(t);
exact = @(t) exp(mu*t)+cos(t);
[t,y_m] = dd2(f_m,[0, 1],exact(0), exact(h), h);
plot(t, exact(t)); hold
Current plot held
plot(t,y_m);
%plot(t,y,'-o');
xlabel('t')
ylabel('y')
title('When h = 0.01 and µ=20')
%------------------------------------------------------
% 2-step Predictor-Corrector
% [T,Y]=dd2(f,definition,y,h); definition=[t1,tfinal]
%------------------------------------------------------
function [T,Y] = dd2(f, definition, Y1, Y2, h)
t1 = definition(1); tfinal = definition(2); t = t1:h:tfinal;
T = t(1:2)'; Y = [Y1;Y2];
for i = 2:numel(t)-1
P = Y(i) + h/2*(3*f(t(i),Y(i))-f(t(i-1),Y(i-1)));
Y(i+1) = Y(i) + h/12*(5*f(t(i+1), P) + 8*f(t(i),Y(i)) - f(t(i-1),Y(i-1)));
T=[T;t(i+1)];
end
end
%
Lateef Adewale Kareem on 30 May 2022
Edited: Lateef Adewale Kareem on 30 May 2022
yeah. he should have sent it in. I have modified the solution to use the exact solution at h