This works as any other function - simply create a file with [OUT parameters] = function my_fun(IN parameters), save it to the Matlab path and you can call it as you like. Alternatively, if you are looking for more advanced input/output manipulation you can use nested function/global variable/structures/... (check the manual http://uk.mathworks.com/help/matlab/function-basics.html)

You might have to declare an event function in matlab such that at every step the function f is integrated first and the solution used in the integration of dy/dx.  Another alternative is to write a nested function.  Let me see if i can write a minimal example.

You might have to declare an event function in matlab such that at every step the function f is integrated first and the solution used in the integration of dy/dx.  Another alternative is to write a nested function.  Let me see if i can write a minimal example. 

Hello David Cho

  In the calculation of the function f you mentioned time step. Thus, y is a function of both x and t. In that case you are dealing with a system of  nonlinear partial differential equations and dy/dx should have been written as ∂y/∂x. Depending on the nature of the governing  equation for f the problem can be solved using finite difference or finite element method.  Unless you are saying that f is a function of t only which will be suspicious in a system of linked equations.