Solving two systems of DEs using the ode45 function.

Question

Vassil Botev 2014-7-22

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https://ww2.mathworks.cn/matlabcentral/answers/142957-solving-two-systems-of-des-using-the-ode45-function

评论： Vassil Botev 2014-7-23

I am trying to solve two systems of differential equations in variables x1, x2, x3 using the ode45 function. The equations are given below:

dx1=-2*lambda*beta*x1+2*lambda*alpha*x2+lambda^2*sigma^2;

dx2=beta*x1-(alpha+lambda*beta)*x2+lambda*alpha*x3;

dx3=2*beta*x2-2*alpha*x3;

where alpha=alpha0+alpha1*t and beta=beta0+beta1*t and alpha0, alpha1, beta0, beta1, sigma, lambda are known constants.

The values I am trying to find are X1, X2 and X3. The derivatives of these desired values are given by:

dX1=beta*x1;

dX2=alpha*x2;

dX3=x3;

I am having difficulties implementing the above using the ode45 function given that the problem is defined by two sets of simultaneous differential equations. Any suggestions as to how this can be solved would be much appreciated. Thanks.

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Answer 1

Mischa Kim 2014-7-23

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https://ww2.mathworks.cn/matlabcentral/answers/142957-solving-two-systems-of-des-using-the-ode45-function#answer_146090

在 MATLAB Online 中打开

Vassil, check out

 function my_ode()
 alpha0 = 1;
 alpha1 = 1;
 beta0  = 1;
 beta1  = 1;
 lambda = 1;
 sigma  = 1;
 param  = [alpha0; alpha1; beta0; beta1; lambda; sigma];
 [t,X] = ode45(@EOM,[0 5],[1 2 3 4 5 6],[],param);
 plot(t,X(:,1))
 grid
 end
 function dX = EOM(t,x,param)
 x1     = x(1);
 x2     = x(2);
 x3     = x(3);
 alpha0 = param(1);
 alpha1 = param(2);
 beta0  = param(3);
 beta1  = param(4);
 lambda = param(5);
 sigma  = param(6);
 alpha  = alpha0+alpha1*t;
 beta   = beta0+beta1*t;
 dx1 = -2*lambda*beta*x1+2*lambda*alpha*x2+lambda^2*sigma^2;
 dx2 = beta*x1-(alpha+lambda*beta)*x2+lambda*alpha*x3;
 dx3 = 2*beta*x2-2*alpha*x3;
 dX1 = beta*x1;
 dX2 = alpha*x2;
 dX3 = x3;
 dX  = [dx1; dx2; dx3; dX1; dX2; dX3];
 end