Numerical solution of non-linear model

hi all;

I have a model for liquid level in a tank as;

dh/dt = (F/dA) - (B*sqrt(h))/dA,

Where B,d,A are constants,

I want to get the numerical solution for a step input change in F, say 0.4

using Euler method or any other suitable numerical method.

Thanks.

[José-Luis]

How is d a constant? Isn't your equation a differential equation?

[Bdayz]

Hello José-Luis,

d actually stands for density, should have capitalized it to help in the understanding,sorry.

Thanks

Answer 1

[Luca Fenzi]

I think that equation can be recast as: h'(t)=(F/dA) - (B*sqrt(h(t)))/dA, d,B,A,F constants Instead of using Euler method I will prefer the buil in function ode23 or ode4, since they will provide you better simulations

% Parameters of the model
B=1; 
A=1; 
F=1; 
d=1;
% Parameters for the simulations
tspan=[0,5] % time interval of the simulations
h0=0; % Intial data
% simulation with ode23
[t,h] = ode23(@(t,h) F/(d*A) - B*sqrt(h)/d*A, tspan, h0);
% simulation with ode45
% [t,h] = ode23(@(t,h) F/(d*A) - B*sqrt(h)/d*A, tspan, h0);

% Show the results:
plot(t,h)
xlabel('t')
ylabel('h(t)')

[Bdayz]

Hi Luca Fenzi,

Thanks very much for the response, got my way around it, am now struggling with the temperature response for now. Hope you can be of help?

[Luca Fenzi]

I did not understand your question, what variable is the temperature? (h(t)?)