How can I solve the coupled differential equation with variable coefficients?
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Vellapandi M Research Scholar
el 8 de En. de 2020
Respondida: Dinesh Yadav
el 22 de En. de 2020
I try to solve coupled differential equation in matlab. This is the code I was typed in matlab
syms u(t) v(t)
ode1 = diff(u) == v;
ode2 = diff(v) == ((5/sqrt(2))*exp((1-sqrt(2))*t)-(5/sqrt(2))*exp((1+sqrt(2))*t)+1)*u + (((5*(1-sqrt(2)))/sqrt(2))*exp((1-sqrt(2))*t)-((5*(1+sqrt(2)))/sqrt(2))*exp((1+sqrt(2))*t)+2)*v;
odes = [ode1; ode2]
cond1 = u(0) == 1;
cond2 = v(0) == 0;
conds = [cond1; cond2];
[uSol(t), vSol(t)] = dsolve(odes,conds)
In command window
Warning: Unable to find explicit solution.
> In dsolve (line 190)
In coupled (line 8)
Error using sym/subsindex (line 855)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be symbolic variables, and function body must be sym expression.
Error in coupled (line 8)
[uSol(t), vSol(t)] = dsolve(odes,conds)
Can someone help me with this error? Thank you.
5 comentarios
David Goodmanson
el 9 de En. de 2020
that's right. Matlab can't solve it symbolically, but there is always numerically..
Respuesta aceptada
Dinesh Yadav
el 22 de En. de 2020
Hi Vellapandi,
Continuing from David Goodmanson's comment you can solve it numerically. Below is the code for it.
tspan = [0 5];
y0=[1;0];
[uSol, vSol] = ode45(@(t,x) [x(1);((5/sqrt(2))*exp((1-sqrt(2))*t)-(5/sqrt(2))*exp((1+sqrt(2))*t)+1)*x(2) + (((5*(1-sqrt(2)))/sqrt(2))*exp((1-sqrt(2))*t)-((5*(1+sqrt(2)))/sqrt(2))*exp((1+sqrt(2))*t)+2)*x(1)],tspan,y0)
You can change the time limits as per your application.
You can refer to documentation link below to see how to solve system of differential equations.
Hope it helps.
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