Solve this equstion by using IMPLICIT method in Partial Differential Equations:

with a MATLAB soulotion

1.5 Example: Heat Transfer (Implicit Method) The conservation of heat can be used to develop a heat balance for a long, thin rod. If the rod is not insulated along its length and the system is at a steady state, the equation that results is d' T dra + h (Ta - T) = 0 where h is a heat transfer coefficient that parameterizes the rate of heat dissipation to the surrounding air and Ta is the temperature of the surrounding air. T T2 :0 X = For a 10-m rod with Ta = 20, 71 = 40, 72 = 200, and h = 0.05, it is called a boundary value problem (BVP) since the value of the function at the boundaries is known. The second order differential equation can be approximated as Titi - 2 +Ti-1 ~ _h(Ta - Ti) or Titi - 2Tit Ti-1~-Ax"h(Ta - T.) or Ti-1 - (2+ Arch)Ti + Ti+1 = -Ax/hTa