Solution of a PDE Using the Differential Transformation Method
Solution of a PDE Using the Differential Transformation Method
Consider the partial differential equation (PDE) =αu with initial condition and boundary conditions and , , and , where is the thermal diffusivity. This problem represents the transient heat conduction in a slab. This Demonstration obtains the temperature profile for user-set values of the dimensionless time and the thermal diffusivity . The red curve and the dashed blue curve are obtained using Mathematica's built-in function NDSolve and the differential transformation method (DTM), respectively. Here, the DTM gives reasonably good results despite its simplicity.
∂u
∂t
2
∂
∂
2
x
t≥0
-1≤x≤1
u(x,0)=0
u(1,t)=u(-1,t)=1
α
u(x,t)
t
α