I am trying to solve 3 simultaneous ODE's. Which method to use?
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Dhiraj Deshmukh
am 6 Sep. 2021
Kommentiert: Dhiraj Deshmukh
am 7 Sep. 2021
I am trying to solve 3 simultaneous ODE's. Which method should be used to solve these equations?? I have tried to solve it using ode45 method but I'm unable to get the answer.
dx1/df = F( f, x1, x2, x3 ) ]
dx2/df = F( f, x1, x2, x3 )
dx3/df = F( f, x1, x2, x3 )
f = [0.5 1]
x1(0.5)=0.185, x2(0.5)= 0.285, x3(0.5)= 0.53
gamma = 0.577;
xo1= 0.185; xo2= 0.285; xo3 =0.53;
theta=0.5;
q1=1; q2 = 0.317; q3 = 0.065;
F(x1,f) = ((q1)*(x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta)))-x1*(x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta))+q2*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))+q3*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta))))*f)/(((x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta)))+q2*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))+q3*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta))))*f);
F(x2,f) = ((q2)*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))-x2*(x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta))+q2*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))+q3*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta))))*f)/(((x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta)))+q2*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))+q3*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta))))*f);
F(x3,f)= ((q3)*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta)))-x3*(x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta))+q2*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))+q3*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta))))*f)/(((x1-gamma*(x1*f-(xo1*(1-theta)))/(f-(1-theta)))+q2*(x2-gamma*(x2*f-(xo2*(1-theta)))/(f-(1-theta)))+q3*(x3-gamma*(x3*f-(xo3*(1-theta)))/(f-(1-theta))))*f);
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Paul
am 6 Sep. 2021
This line:
dy = zeros(4,1);
Needs to be replaced with:
dy = zeros(3,1);
After that, note that the equation for dy(1) evaluates to NaN at f = 0.5 and to -Inf at f = 0 (I only explored between 0 and 1). In the original question it was stated that the the tspan input to ode45 is [0.5 1]. So that will cause a problem because the initial value of dy is NaN at f = 0.5 and that kills the entire solution. I ran from [0.51 1] and got a non-NaN result. In the follow up comment the user enters the tspan limits. If those limits cause the solver to hit either f = 0 or f = 0.5 exactly there will be a problem. So I guess the real question is if it's expected that the equations for dy have these singulariites and how they should be handled if the solver has to integrate through them.
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Steven Lord
am 6 Sep. 2021
This documentation page includes two examples, the second of which you can use as a model for your code to solve a system of differential equations.
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