Can someone help me to identify the formula on the attached image?

[t0mm02]

Homework Statement

2D diffusion equation model using the Explicit Finite Difference Method

Relevant Equations

Lapace Equation, 2D Diffusion Equation

I have to do a MATLAB assignment but when it comes to the report (the theory) I am having quite a lot of problems. My tutor used this formula that I am going to attach:

However, I don't know if that equation is the Laplace equation, the 2D Heat Diffusion equation, or what exactly that is as I can not find it anywhere like he wrote it on there.

 

[pasmith]

That's the heat equation. Multiplying both sides by $\alpha$ gives the standard form $$\frac{\partial T}{\partial t} = \alpha\left(\frac{\partial^2 T}{\partial x^2} + <br /> \frac{\partial^2 T}{\partial y^2}\right)$$

 

[t0mm02]

That's the heat equation. Multiplying both sides by $\alpha$ gives the standard form $$\frac{\partial T}{\partial t} = \alpha\left(\frac{\partial^2 T}{\partial x^2} +<br /> \frac{\partial^2 T}{\partial y^2}\right)$$

If it was only alpha in stead of 1/alpha I would understand it. Why is it 1/alpha?

 

[Mark44]

If it was only alpha in stead of 1/alpha I would understand it. Why is it 1/alpha?

What is it you don't understand? These two equations are equivalent.
$$\frac{\partial T}{\partial t} = \alpha\left(\frac{\partial^2 T}{\partial x^2} +
\frac{\partial^2 T}{\partial y^2}\right)$$
$$\frac 1 \alpha\frac{\partial T}{\partial t} =\frac{\partial^2 T}{\partial x^2} +
\frac{\partial^2 T}{\partial y^2}$$

By the way, problems involving derivatives or partial derivatives are NOT precalculus. Please post any such problems in the Calculus & Beyond homework section or in one of the Physics homework sections.