I need help getting started on a program for the heat equation... namely the equation ut = k*uxx

I usually start with


But seriously, in order to write a program, you have to define the problem and decide on a method. Sometimes it is called a Program Specification. See footnote.

What are the inputs? What are the outputs? What method will you use to process the inputs in order to obtain the outputs?

The heat equation is a second order differential equation where you have a function u(t, x) that satisfies the equation that you tried to represent (it's hard without real typesetting symbols, but we know what equation you mean).

The equation by itself is clearly inadequate to use to get a solution (other than the trivial one of zero everywhere and all of the time). Unless we are applying this equation to the Universe at large, there have to be some other "givens". Typically boundary conditions for schoolboy problems like this are given in the form

u(0, x) = f(x) for 0 <= x <= L (the initial distribution of heat over a finite range of x)

u(t, 0) = u(t, L) = 0 (value at the end points)

Joseph Fourier published solutions for several cases early in the 18th century (yes, without a computer other than his "little gray cells", as that other great Frenchman Hercule Poirot would say).

There are a number of numerical methods for solving second order boundary value problems. Which would you like to use?

What is the context of your assignment? Computer Science? Math? Mechanical Engineering? What? What are the prerequisites? Do you have any background in Numerical Analysis?

Or was a method suggested (assigned)?

Regards,

Dave

"Ya gotta have a plan."
---davekw7x