heat flow finite difference

49 Views Asked by At

I'm trying to solve one dimension heat flow equation using finite difference and I feel like I'm making a huge mistake somewhere and I have no idea where.

I have a assumed a boundary condition and a set of initial values of temperatures at time = 0

I then use equation 1 to obtain second partial derivative of heat equation by x from my initial values

According to heat equation 2 the first partial derivative of heat equation by time is equal to second partial derivative by x.

Shouldn't then multiplying the the first partial derivative by delta-time give me the new temperatures at time t plus delta?

It sounds so intuitive for me but when I plug all of this into excel, the values calculated are far from reasonable.

Central finite difference for second derivative