derv:=proc(neqn,t,u,ut) # # Function derv computes the derivative vector # of the nonlinear PDE # # Type variables local u0, dx, dxs, i, alpha, k, sigma, L, ui, ua, a, e, rhos, cps, ls, cs: # # Problem parameters alpha:=1.0e-06: k:=1.0: sigma:=5.67e-08: L:=0.1: ui:=298.0: ua:=2000.0: a:=1.0: e:=1.0: rhos:=7800.0: cps:=435.0: ls:=0.025: cs:=rhos*cps*ls: # # Spatial grid dx:=1.0/(neqn-2): dxs:=dx*dx: # # Insulation for i from 1 to neqn-2 do if(i=1)then u0:=u[2]+2.0*dx*L*(sigma/k)*(a*ua^4-e*u[1]^4): ut[1]:=(u[2]-2.0*u[1]+u0)/dxs: else ut[i]:=(u[i+1]-2.0*u[i]+u[i-1])/dxs: end if: end do: # # Steel ut[neqn]:=(k*L/alpha)*(1.0/cs)*(u[neqn-2]-u[neqn-1])/dx: ut[neqn-1]:=ut[neqn]: # # End of derv end: