I am trying to generate these 3 plots

Question

Mr.DDWW 2022-3-3

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1662610-i-am-trying-to-generate-these-3-plots

回答： Walter Roberson 2022-3-3

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Mr.DDWW 2022-3-3

在 MATLAB Online 中打开

clc;clear all;

n=100000;

alphat=1;

y_b=linspace(0,1);

% y_b=.1

for j=1:length(y_b)

sum_D=0;

for i=1:n

sum_D=sum_D+(((-1)^(i-1))/(((i-1)+0.5)*pi))*exp(-((i-1)+0.5)^2*pi^2*alphat)*cos((i-1)+0.5)*pi*y_b(j);

end

F(j)=2*sum_D;

end

plot(y_b,F);grid on;

I tried but not correct

Walter Roberson 2022-3-3

在 MATLAB Online 中打开

Regardless of the theoretical shape, you can see from the below with very reduced n that after n = 2, the terms are too small to make any difference in the summation.

n=5.0000;

alphat=1;

y_b=linspace(0,1,10);

% y_b=.1

Pi = sym(pi);

for j=1:length(y_b)

sum_D = sym(zeros(1,n));

for i=1:n

sum_D(i)=(((-1)^(i-1))/(((i-1)+0.5)*Pi))*exp(-((i-1)+0.5)^2*Pi^2*alphat)*cos((i-1)+0.5)*Pi*y_b(j);

end

vpa(sum_D)

F(j)=2*sum(sum_D);

end

ans =

F(1:min(end,10)).'

ans =

vpa(ans)

ans =

plot(y_b,F);grid on;

simplify(F ./ F(2))

ans =

vpa(ans)

ans =

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Answer 1

Walter Roberson 2022-3-3

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1662610-i-am-trying-to-generate-these-3-plots#answer_909164

在 MATLAB Online 中打开

        sum_D(i)=(((-1)^(i-1))/(((i-1)+0.5)*Pi))*exp(-((i-1)+0.5)^2*Pi^2*alphat)*cos((i-1)+0.5)*Pi*y_b(j);

Look at that. How does the change of j affect it ?

j does not show up until y_b(j) which is a multiplier. And it is constant for all the different I values. So the result is going to be same as if you calculated for all the i values without including the y_b(j) term, and then multiplied by the y_b(j) term afterwards.

Which means that the result is going to be exactly the same each time, except multiplied by y_b(j) . And since the y_b is linear, that means you get a linear result.