# Compute the Green's function for one dimensional Laplacian operator?

Posted 8 months ago
726 Views
|
|
1 Total Likes
|
 I am trying to compute the Green's function for one dimensional Laplacian operator. The command I'm using is- GreenFunction[Laplacian[u[x],x], u[x], x \[Element] FullRegion[1], m] There is no result for this command, However when I'm using this command for two dimensional case- GreenFunction[ Laplacian[ u[x, y], {x, y}], u[x, y], {x , y} \[Element] FullRegion[2], {m, n}], Mathematica is giving me the correct result. Can someone please help?
Sort By:
Posted 8 months ago
 This is not well defined on the whole axis In[1]:= G = GreenFunction[{Laplacian[u[x], {x}], u[a] == 0, u[b] == 0}, u[x], {x, a, b}, m] Out[1]= -(((b - m) (a - x) HeavisideTheta[m - x])/( a - b)) - ((a - m) (b - x) HeavisideTheta[-m + x])/(a - b) In[2]:= G1 = Limit[G, {a -> -Infinity}] Out[2]= -b HeavisideTheta[m - x] + m HeavisideTheta[m - x] - b HeavisideTheta[-m + x] + x HeavisideTheta[-m + x] In[3]:= G2 = Limit[G1, {b -> Infinity}] Out[3]= \[Infinity] (-HeavisideTheta[m - x] - HeavisideTheta[-m + x]) 
Community posts can be styled and formatted using the Markdown syntax.