In this talk, we will present an approach to construct the Green’s function for an initial boundary value problem with precise pointwise structure in the space-time domain. This approach is given in terms of transform variable and physical variable. The mixed algebraic structure in the transform variable gives the large time asymptotic nature of the differential equation. One also uses the algebraic structure in the fundamental solution. Finally, the hybrid of transform variable and physics variable to a precise pointwise space-time structure of the solution of an initial boundary value problem.