MATLAB: User-defined function as input in “dsolve”

dsolve user-defined functions

Hello everyone, I am new with MATLAB so maybe I can do the following and still haven't figured out how.

I want to use

dsolve ('Dz=a*z+b*t+c(z,t)','t')

where a and/or b are symbolic and

c(z,t) is a user-defined function?

The specific form of the expression is only an example (in principle it could/should be more general. The important thing here is the use of a user-defined function within the expression that defines the differential equation to be solved.

Is there any way I ca do something to this effect?

Best Answer

I think I found the way - it was hidden in an example about using dsolve for a system of ODE that are extracted from a matrix!!

Anyway...

So suppose you have a defined a function r(x,y) (either directly with inline or anonymous function, or extracting from a solution of a previous system, matrix etc)

Then as I understand it you create the string of it

eq=char(r(x,y))

[note if r(x,y) corresponds to a solution ans.w of a previous system then one can define the string eq diectly as eq=char(ans.w)]

and then you use dsolve as follows

dsolve(strcat('Dx=',eq),'t')

[where t is the independent variable (which could be y)]

stracat(s1,s2) is a built-in function that "keeps together" the two strings (in general more than two) 'Dx=' and eq creating a new string that corresponds to the symbolic expression implied by Dx=r(x,y).

It has worked for few examples I played with, but maybe there is a flaw in this I cannot see, or maybe there is a more efficient way of doing it.

Related Solutions

MATLAB: Simplifying symbolic expressions using assumptions

I don’t think there is a way to directly approximate a symbolic expression in MATLAB with another symbolic term.

However, here is a workaround for the example you provided. Since x*y >> 1, you may want to consider replace (x*y+1) with x*y by using the function sub (See Documentation) .

For example, the following code can be executed

>> syms x y
>> A = x/(x*y+1);
>> A = subs(A, 'x*y+1', 'x*y');

The result will be A = 1/y.

-Yu

MATLAB: How to do the following

This is really not complicated. So far you've only implemented one half of any statement. Maybe spend more time understanding the statement?

E.g., for the first one: If the color of v(x,y) is black and the colors of q(x,y) and r(x,y) are both white, one of q(x,y) and r(x,y) is selected with equal probability, and the selected pixel is set to black.

if V(x, y) == 0 && q(x, y) == 1 && r(x, y) == 1  %Implements: If the color of v(x,y) is black and the colors of q(x,y) and r(x,y)
   if rand >0.5      %implements: one of q(x,y) and r(x,y) is selected with equal probability and set to black
        q(x, y) = 0;
   else
        r(x, y) = 0;
   end
end

Best Answer

Related Solutions

MATLAB: Simplifying symbolic expressions using assumptions

MATLAB: How to do the following

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