The present article is an extension of the previous article based on the statistical transition matrix B which aimed to study the steady-state solution of the ICBC distribution in the diffusion PDE. We extend here the same theory to find the spatio-temporal evolution of the energy density vector. Numerical results of the required solution are presented for 2D and 3D configuration space problems where the precision and convergence speed or computation time are superior to the conventional method of separating variables and numerical finite difference techniques