Plot polynomial using Eueler's method

Question

E 2022-10-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1820265-plot-polynomial-using-eueler-s-method

编辑： E 2022-10-9

采纳的回答： Davide Masiello

syms x;

y=x.^3 + x.^2- 12*x; %polynomial function

dy= diff(y,x)%derivative of y

N=100;

h=0.1;

x=-4:0.1:3;

y(1)=-10;

y=zeros(size(x));

EM=[]; %empty array to store values

for n=1:N

y(n+1)=y(n)+h*dy(n);

x(n+1)=n*h;

EM(x,y)=[x,y];

end

plot(EMsub,"r-")

Hello, this is the code that i have so far. I have tried writing a code to plot f(x)=x^3+x^2-12x using Euler's method in matlab. I can seem to figure out why the code is not running. At line 12 i keep getting the following error:

Error using symengine

Unable to convert expression containing symbolic variables into double array. Apply 'subs' function first to substitute values for variables.

I am not exactly sure how to fix this error or what is wrong. Could someone explain why its not working and what i am doing wrong here? Any help would be appreciated.

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Answer 1

Davide Masiello 2022-10-8

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1820265-plot-polynomial-using-eueler-s-method#answer_1069645

编辑：Davide Masiello 2022-10-8

在 MATLAB Online 中打开

so, initially, you calculate the analytical derivative of the function using the symbolic environment

syms x

y = x^3+x^2-12*x; % polynomial function

yp = diff(y,x) % symbolic derivative of y

yp =

You'll need this symbolic derivative to be turned into a matlab function, which you can to like this

dydx = matlabFunction(yp)
dydx = function_handle with value:
    @(x)x.*2.0+x.^2.*3.0-1.2e+1

Now, you can solve the ODE represented by dydx using Euler's method.

h       = 0.1;
xn      = -5:h:5;
yn      = zeros(size(xn));
yn(1)   = -40;
for idx = 2:length(xn)
    yn(idx) = yn(idx-1)+h*dydx(xn(idx-1));
end

Now, you can plot both numerical and analytical solutions for comparison

fplot(y)

hold on

plot(xn,yn,'k--')

legend('Analytical solution','Euler''s method')

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John D'Errico 2022-10-8

编辑：John D'Errico 2022-10-8

在 MATLAB Online 中打开

@E

Your code was not terrible. But you need to worry more about what variables you use, and about moving from the symbolic side of MATLAB, to the numerical side. For example,

syms x;

y=x.^3 + x.^2- 12*x; %polynomial function

dy= diff(y,x)%derivative of y

dy =

At this point, y and dy are symbolic expressions in MATLAB.

whos y dy
  Name      Size            Bytes  Class    Attributes

  dy        1x1                 8  sym                
  y         1x1                 8  sym                

But then later on, you tried to use y to store a vector of numbers, as the solution to the ODE. That might cause a problem. ;-) Be careful about re-using the same variable names. Yes, you did reassign y. But what did you do?

y(1)=-10;

So, first, you assigned the initial condition to y. But that does not actually do what you think. It overwrites the symbolic function y that you created.

y

y =

And THEN you essentially did this:

x=-4:0.1:3;
y=zeros(size(x));

So you have now lost the information about the initial condition you tried to enforce, because you have now just overwritten the variable y.

As far as the code by Davide goes, you ask why N was started at 2. Since you already know the value of y(1), you don't need to use the Euler step to compute y(1) at all. So that only applies to the values y(2) through y(N).

But as I said, your code was not too far from actually working. I would say you mainly need to take a little more care, thinking about what your variables store, and exactly what they mean at that point in time. As well, I'd be willing to use new variable names, to avoid confusion in your code.

E 2022-10-8

编辑：E 2022-10-9

Thank you so much everyone for your helpful feedback. Seeing my code not working and not knowing why was truly frustrating. Matlab is a challenge. I read your comments and i think i understand where my code was running into issues. Thank you again for your help on this.

Steven Lord 2022-10-9

Since it sounds like you're new to MATLAB, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

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Plot polynomial using Eueler's method

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Plot polynomial using Eueler's method

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