Question

Consider the one-dimensional heat conduction equation. Apply forward difference method to approximate time rate and central difference method to approximate x-derivative. The resulting equation is in _____________

(a) Implicit linear form

(b) Explicit linear form

(c) Explicit non-linear form

(d) Implicit non-linear form

Answer 1

Correct answer is (b) Explicit linear form

Best explanation: The one-dimensional heat conduction equation is

(frac{partial T}{partial t}=α frac{partial^2 T}{partial t^2} )

Applying the difference approximations,

(frac{T_i^{n+1}-T_i^n}{Delta t}=alpha frac{T_{i+1}^n-2T_i^n+T_{i-1}^n}{(Delta x^2)} )

(T_i^{n+1}=T_i^n+alphafrac{Delta t(T_{i+1}^n-2T_i^n+T_{i-1}^n)}{(Delta x^2)} )

The equation is in explicit linear form.