How to solve a system of 3 ODE and a linear equation.

How to solve a system of 3 ODE

dvdt=z;

dzdt=-v/(L0*C0)-z*R0/L0

dTempdt=R0*((C0*z)^2)/(m_ponte*Cp_Al)

and one linear equation: R=R0*(1+Alfa*(temp(i)-T0)) to consider the resistence variation with temperature instead of constant resistence R0?

F=@(t, v, z, temp) [z; -v/(L0*C0)-z*R0/L0; R0*((C0*z)^2)/(m_ponte*Cp)];

v(1)=-20000;

z(1)=0;

temp(1)=298;

t(1)=0;

for i=1:N

k1 = h*F(t(i), v(i), z(i), temp(i));

k2 = h*F(t(i)+h/2, v(i)+k1(1)/2, z(i)+k1(2)/2, temp(i)+k1(3)/2);

k3 = h*F(t(i)+h/2, v(i)+k2(1)/2, z(i)+k2(2)/2, temp(i)+k2(3)/2);

k4 = h*F(t(i)+h, v(i)+k3(1), z(i)+k3(2), temp(i)+k3(3));

v(i+1) = v(i) + (1/6)*(k1(1)+2*k2(1)+2*k3(1)+k4(1));

z(i+1) = z(i) + (1/6)*(k1(2)+2*k2(2)+2*k3(2)+k4(2));

temp(i+1) = temp(i) + (1/6)*(k1(3)+2*k2(3)+2*k3(3)+k4(3));

end

Answer 1

[Shadaab Siddiqie]

From my understanding you want to solve an 3rd degree ODE equations. You can go through solve ODE, symbolic variables and expressions and also dsolve for more information.