How to do you use matlab to solve this?

[ngheo1128]

How to do you use MATLAB to solve this?
dh/dt = 0.079577-0.066169*squareroot(h)
where ho = 1.75 and hf = 1.46 and to=0

 

[Simon Bridge]

Welcome to PF;
There are a number of numerical methods.

If we write D as the operator for d/dt, then your problem has form Dh=b-ah,
You know you can write operators and constants as matrices and h as a vector... do that and you have an equation that MATLAB can handle.

 

[hunt_mat]

You could write a method from scratch, you have two boundary conditions but only 1 constant to play with.

 

[NegativeDept]

MATLAB has several built-in ODE solvers. The instructions are here.

I think you have to write ODEs in the form
$\frac{d\mathbf{h}}{dt} = \mathbf{g}(t,\mathbf{h})$
where $\mathbf{h}$ is the thing you're trying to find and $t$ is the independent variable. In your case, $\mathbf{h}$ and $\mathbf{g}$ are one-dimensional, and your ODE is already in the form we want.

Define a function handle for $\mathbf{g}$ like this:

generator = @(t,h) 0.079577-0.066169*sqrt(h)

You don't have to name it "generator," but I always do. (It's a group-theory thing.)

Now call ode45 and give it a start time, stop time, and initial condition:

[times,solution] = ode45(generator,[0,1.46],1.75)

That will start at $t=0$, stop at $t=1.46$, and use the initial condition $h(0) = 1.75$. It produces two columns named times and solution. times is a list of sample times at which $h(t)$ was calculated, and solution is a list of values of $h(t)$ at those times. (You also don't have to call them "times" and "solution.")

 

[alphy]

MATLAB is a powerful tool for solving mathematical equations and models. To use MATLAB to solve the equation provided, you will need to first define the variables and their initial values. In this case, ho = 1.75 and hf = 1.46 and to = 0. Next, you will need to create a function that represents the equation dh/dt = 0.079577-0.066169*squareroot(h). This can be done using the "function" keyword in MATLAB. Once the function is defined, you can use the "ode45" function to numerically solve the equation and plot the results. This function takes in the defined function, the initial values, and the range of time for which you want to solve the equation. The output will be a graph showing the change in h over time. Additionally, you can use the "fzero" function to find the specific value of h at which the equation is equal to 0. This can be useful for finding the steady state solution of the equation. Overall, MATLAB provides a versatile and efficient way to solve mathematical equations and models.