making a table of my results from AdamsBashforth function

Question

Seungryul Lee 2022-5-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1709415-making-a-table-of-my-results-from-adamsbashforth-function

编辑： Torsten 2022-5-1

**How do I make a table of results that includes h and the error: Eh = max|y(t) − y ̃(t)|, where y ̃ is my approximated solution? I'm using Adams Bashforth function with startingtimet =0, endingtimet =20, and stepsizes: h= 1/2^n for n=1, . . . , 10.

f=@(t,y) -y-3*t;
F=@(t) 3-3*t-2*exp(-t);
t0=0; y0=1;
te=20;
nn=1:10;
for ii=1:length(nn)
    n=nn(ii);
    h=1./(2^n);
    [ys, ts] = MyAdamsBashforth2(f, t0, te, y0, h);
    %what should I put here
end   

********************************************

this is my function code

function [ys, ts] = MyAdamsBashforth2(f, t0, te, y0, h)
ts = (t0:h:te).';
ys(1,1) = y0;
reqsteps = (te-t0)/h;
ys(2,1) = ys(1,1) + h*f(ts(1,1),ys(1,1));
for n = 3:reqsteps+1
    ys(n,1) = ys(m-1,1) + h*(3/2)*f(ts(n-1,1),ys(n-1,1)-(1/2)*f(ts(n-1,2),ys(n-2,1)));
end
end				

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Answer 1

Torsten 2022-5-1

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1709415-making-a-table-of-my-results-from-adamsbashforth-function#answer_955100

编辑：Torsten 2022-5-1

在 MATLAB Online 中打开

f=@(t,y) -y-3*t;
F=@(t) 3-3*t-2*exp(-t);
t0=0; y0=1;
te=20;
nn=1:10;
h = 1./2.^nn;
for ii=1:length(nn)
    [ys, ts] = MyAdamsBashforth2(f, t0, te, y0, h(ii));
    Eh(ii) = max(abs(F(ts)-ys));
end
plot(nn,Eh)
T = table(h,Eh);
function [ys, ts] = MyAdamsBashforth2(f, t0, te, y0, h)
ts = (t0:h:te).';
ys(1,1) = y0;
reqsteps = (te-t0)/h;
ys(2,1) = ys(1,1) + h*f(ts(1,1),ys(1,1));
for n = 3:reqsteps+1
    ys(n,1) = ys(n-1,1) + h*((3/2)*f(ts(n-1,1),ys(n-1,1))-(1/2)*f(ts(n-2,1),ys(n-2,1)));
end
end

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Seungryul Lee 2022-5-1

Thanks.

Can you also figure out why I'm getting an error for

reqsteps = (te-t0)/h;

this line?

It says the matrix dimensions should agree to use in my for loop.

Do you know how should I fix it?

Torsten 2022-5-1

编辑：Torsten 2022-5-1

I adapted the code.

There was still an error in the Adams-Bashford update.

I adapted the code once more.

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making a table of my results from AdamsBashforth function

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making a table of my results from AdamsBashforth function

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