How to solve the differential equation numerically

My equation is this:

(-Vs/500)-((6e-10)*diff(Vs,t))+(7/250)+(7.226*Vs*((Vs/1000)+((3e-10)*diff(Vs,t))-7/500)^2)-(3/25000)*(Vs^2)-((4.336e-9)*diff(Vs,t))-(0.014*Vs)-((1.08e5)*((Vs/1000)+((3e-10)*diff(Vs,t))-7/500))+0.2023=0

Vs(0)=7.9

I tried using dsolve but there is no explicit solution. I need solved vector with numerical values for Vs with constant rise in 't'.

Can anyone please help me?

[J. Alex Lee]

this looks like an ODE, and looks like it may be made explicit in d(Vs)/d(t), but it's hard to tell the way it is written. try to write it out in with your numeric parameters replaced by some symbols and do some algebra to figure it out. even if it turns out to be implicit, some of the matlab ode solvers can handle it.

[James Tursa]

Please show us the differential equation you are trying to solve.

[Saurav]

 ode=2*((Cs*diff(Vs,t))-(-Vs+Vdc)/Rmet)==kn*((2*A*Vs)-(((Cs*diff(Vs,t))-(-Vs+Vdc)/Rmet)*2*A*Rsmin)-(Rsmin*Rsmin*(((Cs*diff(Vs,t))-(-Vs+Vdc)/Rmet)^2))+(2*Vs*Rsmin*((Cs*diff(Vs,t))+(Vs-Vdc)/Rmet))-(Vs*Vs))
 
ode(t) =
 
Vs(t)/500 + (1450710983537555*diff(Vs(t), t))/2417851639229258349412352 - 7/250 == (6207659398485333*Vs(t)*(Vs(t)/1000 + (1450710983537555*diff(Vs(t), t))/4835703278458516698824704 - 7/500))/858993459200000 - (3*Vs(t)^2)/25000 - (16209935408597048091837219925467*diff(Vs(t), t))/4153837486827862102824397063376076800000 - (54013508714495997*Vs(t))/4294967296000000000 - (22817324449185183*(Vs(t)/1000 + (1450710983537555*diff(Vs(t), t))/4835703278458516698824704 - 7/500)^2)/209715200000 + 391082542104575979/2147483648000000000
 

[Saurav]

There is no explicit solution for this diff. eqtn. So I want to solve it numerically with constant step rise in t. I am new to matlab so I dont know how to implement it using ode45

[J. Alex Lee]

By "no explicit solution" I think you mean "no analytical solution".

If diff(Vs(t),t) means and that is the only differential term, your equation still looks "explicit in ", which means you can put your equation in the form

rather than how you have it. I'm not going to go through your equation term by term to verify, you should do so yourself.

Then, you should be able to follow Asvin's advice to look at examples of how to solve that class of problems using ode45.

If your problem is truly "implicit" in , then look at https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html under "Types of ODEs" near the top

Answer 1

[Asvin Kumar]

As others have mentioned in the comments, ODE seems best suited for this problem. Here’s an example from which you can adapt a solution. Solve a Nonstiff Equation using ode45

[Saurav]

yes but problem here is dy/dy is in quadratic form so there will be two solutions for dy/dt. I don't know how to implement it as I am new to matlab.Thank you so much.

[Asvin Kumar]

I see what you're talking about. ode15i is the recommended way to go about these problems. Have a look at this example on solving Weissinger Implicit ODE to get started. This should give you an idea of how you can use the function.

Answer 2

[madhan ravi]

https://www.mathworks.com/matlabcentral/answers/428484-how-can-i-convert-set-of-symbolic-functions-into-function-handle-so-that-they-can-be-used-as-input-t