Scaling of a system of coupled differential equation and is it possible?

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Md. Golam Zakaria 2023-2-9

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https://ww2.mathworks.cn/matlabcentral/answers/1909395-scaling-of-a-system-of-coupled-differential-equation-and-is-it-possible

移动：Torsten 2023-2-9

采纳的回答： Torsten

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Hello everyone.

I have a system of coupled differential equation and I am using ode45 to solve it. The code is as following

clc
clear all
f = @(t,x) [-x(4)-(0.0424)+(1.6977)*exp(-1.48e36*(x(1)^2));
            x(4)-(0.0663)+(2.6540)*exp(-6.0653e35*(x(2)^2));
           -(2.994e5)*x(4);
            3.6999e7*(7.124e17*(x(1)^2)-2.915e17*(x(2)^2)+x(3)+60*(cos(t)))-2.55  3.6999e7*x(4)];
       
[t,xa] = ode45(f,[0, 80],[0,0,-62,0]);

This code is right to my knowledge. The problem is I am facing out of memory problem while running this. Takes too much time and my pc doesnt have enough ram to run it maybe. Now, I do have a sample code from a Professor. The is is as follows

clc
clear all
f = @(t,x) [-x(4)-(1.10*10^-8)+(5.6*10^-6)*exp(-1.35*10^20*(x(1)^2));
            x(4)-(1.10*10^-8)+(5.6*10^-6).*exp(-1.35*10^20*(x(2)^2));
            -(0.23)*x(4);
            -0.40*x(4)+x(3)+11.33*(x(1)^2)-11.33*(x(2)^2)+60*(cos(t))];
[t,xa] = ode45(f,[0, 80],[0,0,-120,0]);

Now the concerning part for me is, if we look closely at the third and fourth equation of both code, the coefficients differ by a huge margin. I am 90% sure that the coefficients I derived are true because they match to a paper. The sample code runs quickly.

Now, my question is, is it possible to scale down a system of differential equation. To me it seems that the sample code is somehow scaled down. Can someone please let me know if it is possible and if possible, how to do it.

Thank you.

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Answer 1

Torsten 2023-2-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1909395-scaling-of-a-system-of-coupled-differential-equation-and-is-it-possible#answer_1167615

移动：Torsten 2023-2-9

If possible, use different units for physical parameters involved such that values like exp(-1.48e36*(x(1)^2)), exp(-6.0653e35*(x(2)^2)), 7.124e17*(x(1)^2), 2.915e17*(x(2)^2) become much, much smaller.