Help with ODE45 Running Forever

Question

Daniel Beeson 2020-10-27

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https://ww2.mathworks.cn/matlabcentral/answers/627163-help-with-ode45-running-forever

评论： Walter Roberson 2020-10-27

Hi everyone,

I'm having a rough time with a line of my ode45 code, it's working for my y and z directions, but not my x-direction, which is weird because my X and Z are practically the same. Did I make any ovbious mistakes? Any ideas why the ode45 can't do my x-direction term?

close all, clear all, clc
vx0 = .1;
vy0 = .1;
vz0 = .1;
E = 10^4;
B = .1;
theta = atan(vx0/(vz0 - E/B));
q = -1.6*10^-19;
m = 9.11*10^-31;
wc = q*B/m;
vth = sqrt(vx0^2 + (vz0 - E/B)^2);
t_span = [0:pi/10:10*pi];
[t1,x] = ode45(@(t,x) (vth*sin((wc*t) + theta)), t_span, vx0);
[t2,y] = ode45(@(t,y) vy0, t_span, vy0);
[t3,z] = ode45(@(t,z) (vth*cos((wc*t) + theta)) + E/B, t_span, vz0);

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Answer 1

Walter Roberson 2020-10-27

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https://ww2.mathworks.cn/matlabcentral/answers/627163-help-with-ode45-running-forever#answer_525218

For t1 you have a sin wave with frequency 17563117453.348 being integrated over 0 to 10*pi . This is a quite high frequency and ode45 needs to take very small steps to try to integrate it properly while maintaining relative accuracy.

For t3, you have a cos wave with frequency 17563117453.348, plus a fair-sized constant. The steps are often noise compared to the constant and ode45 does not have to take many steps to maintain relative accuracy.

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Daniel Beeson 2020-10-27

Is there any real fix to this then since those are the parameters of the problem I am required to plot?

Walter Roberson 2020-10-27

Analytically, the function associated with t1 is about 5.6937e-6*cos(1.7563e+10*T + 1.0e-6) - 5.6937e-6 so it has a frequency of roughly 2E10. You cannot meaningfully plot that for more than a very very short period (a small number of nanoseconds)

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