How i implement Adams Predictor-Corrector Method from general code ?
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Below is the Adams predictor-corrector formula and general code. How can I adapt this code to the above question? Can you please help?
%------------------------------------------------------
% 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 个评论
Hazel Can
2022-5-27
Torsten
2022-5-27
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.
采纳的回答
Lateef Adewale Kareem
2022-5-29
编辑：Lateef Adewale Kareem
2022-5-30
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
plot(t,y_m);
%plot(t,y,'-o');
legend('Exact Solution','Adams predictor-corrector formula')
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
%
4 个评论
Torsten
2022-5-30
You implemented rk4, not rk2.
Torsten
2022-5-30
As far as I read in your assignment, you should use the exact solution for y1. So neither rk2 nor rk4 is needed.
Lateef Adewale Kareem
2022-5-30
编辑：Lateef Adewale Kareem
2022-5-30
yeah. he should have sent it in. I have modified the solution to use the exact solution at h
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