Ode45

Mush · #1 $Old$ October 27th, 2009, 03:36 PM

Hello there.

Okay, let's say I have a system of 1st order ODEs to solve. So I create a function file which describes these functions called, say:

Code:

 function dy = myfunction(t,y)

.

Now, to solve these ODEs using ODE45, I'd simply write a script file which says:

Code:

[t,y] = ode45(@myfunction, [t0 tf], [y10 y20 y30 y40...yn0])

, and ODE45 will perform the integration and spit out the solution in the vector y.

Now let's say I want to do the same thing again, but rather than use ODE45, I'd like to use my own integration scheme. So I begin to write my function file to perform the integration using, say, a modified Euler method. How would I write the file in such a way that it takes the same inputs as ode45, and produces the same outputs? How to I write my integration scheme to use myfunction(t,y)? I'm rather confused about it, and scanning over the ODE45 code to see how ODE45 does it is a bit beyond my scope.

elbarto · #2 $Old$ October 27th, 2009, 05:02 PM

I think you need to look into "function_handles and "anonymous functions" if I understand your question correctly?

Example:

Code:

EDU>> f = @(x)magic(x)

f = 

    @(x)magic(x)

EDU>> f(2)

ans =

     1     3
     4     2

EDU>> f(5)

ans =

    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

EDU>>

Regards Elbarto

Mush · #3 $Old$ October 28th, 2009, 05:26 PM

Blah!

elbarto · #4 $Old$ October 28th, 2009, 05:38 PM

When you pass your function into ode45, you are passing it in as a function_handle. This allowes ode45 to assign its own name to some instance of your function, which in my example I called f. If you already know how to do the integration and want to create a function like ode45, you will need to use function_handles.

This might help:
Function Handles (Programming and Data Types)

You are essentially createing a function_handle when you write

Code:

@mydifferentialequation

Maybe I am still misreading the question? This is the method I used when I wrote my own implementation of newtons method, I let the user pass a function_handle for f(x) and a second function_handle for df/dx.

Elbarto

Mush · #5 $Old$ October 28th, 2009, 07:08 PM

Quote:

Originally Posted by elbarto $View Post$

When you pass your function into ode45, you are passing it in as a function_handle. This allowes ode45 to assign its own name to some instance of your function, which in my example I called f. If you already know how to do the integration and want to create a function like ode45, you will need to use function_handles.

This might help:
Function Handles (Programming and Data Types)

You are essentially createing a function_handle when you write

Code:

@mydifferentialequation

Maybe I am still misreading the question? This is the method I used when I wrote my own implementation of newtons method, I let the user pass a function_handle for f(x) and a second function_handle for df/dx.

Elbarto

Would it be too much to request an excerpt of example code?

Mush · #6 $Old$ October 28th, 2009, 07:40 PM

Got it!