How to use ode45 for an equation with space dependent coefficients?

Question

Mirlan Karimov 2019-3-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/450396-how-to-use-ode45-for-an-equation-with-space-dependent-coefficients

评论： darova 2019-3-16

采纳的回答： darova

Consider an equation of form:

where

so that after each time iteration

I have to update

to be used in the next time iteration. I have hard coded Runge-Kutta scheme but I believe that there are some tolerance problems. Therefore, I want to try ODE45 and check the difference.

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Answer 1

darova 2019-3-16

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/450396-how-to-use-ode45-for-an-equation-with-space-dependent-coefficients#answer_365661

在 MATLAB Online 中打开

p = @(x) sin(x).*sqrt(tan(x));
% x(1) == x
% x(2) == x'
f = @(t,x) [x(2); -p(x(1)).*x(1)];
tspan = [0 2];
x0 = [0.5 0.1];
[t, x] = ode45(f,tspan,x0);
plot(t,x(:,1),'r',t,x(:,2),'b')

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Mirlan Karimov 2019-3-16

Thank you!

I think I should clarify the question a bit more. What if p is a bit more complicated so that cant be directly written as a function? For example, in my case,

where C is a complicated function of x and I is another complicated function obtained by summation of vector cross products?

darova 2019-3-16

在 MATLAB Online 中打开

function main
clc, clear
tspan = [0 1];
x0 = [ 0.1 0.5]
[t,y] = ode45(f,tspan,x0);
X = y(:,1);
Y = y(:,2);
plot(X,Y,'r')
end
function ydot = f(t,x)
x1 - x(1);
dx = x(2);
C = % complicated function
I = % another
    ydot(1) = dx;                      % x'
    ydot(2) = -C/I*x1;               % x''
end