A solution for the neutron diffusion equation in the spherical and hemispherical reactors using the residual power series

Abstract

A novel analytical solution to the neutron diffusion equation is proposed in this study using the residual power series approach for both spherical and hemispherical fissile material reactors. Various boundary conditions are investigated, including zero flux on the boundary, zero flux on the extrapolated boundary distance, and the radiation boundary condition (RBC). The study also shows how two hemispheres with opposing flat faces interact. We give numerical results for the same energy neutrons diffused in pure P239u. By qualitative comparison with the homotopy perturbation method and Bessel function-based solutions, the residual power series method (RPSM) presents accurate series solutions that converge to the exact solutions, as shown in this study. Moreover, numerical results were shown to be improved by the computer implementation of the analytic solutions.

Computational Analysis of Fractional-Order KdV Systems in the Sense of the Caputo Operator via a Novel Transform

“…Fractional-order partial differential equations (FPDEs) have been suggested and studied during the past few decades in a variety of scientific areas, including biology, plasma physics, finance, chemistry, fluid mechanics, and mechanics of materials. In order to better express physical and control systems, systems of fractional partial differential equations have become more and more popular [13][14][15][16][17]. Approximative or numerical techniques are typically used because some fractional-order partial differential equations do not have accurate analytic solutions.…”