The meshless method for solving radiative transfer problems in a slab medium based on radial basis functions

TL;DR

This paper introduces a meshless numerical method using radial basis functions to solve radiative transfer equations in slab media, eliminating the need for mesh generation and demonstrating accuracy and convergence through numerical experiments.

Contribution

It presents a novel meshless approach based on radial basis functions for solving radiative transfer problems, improving computational efficiency and accuracy.

Findings

The method achieves high accuracy in numerical experiments.

It demonstrates convergence through residual norm analysis.

The approach outperforms traditional mesh-based methods.

Abstract

In this paper a numerical meshless method for solving the radiative transfer equations in a slab medium with an isotropic scattering is considered. The method is based on radial basis functions to approximate the solution of an integral-partial differential equation by using collocation method. For this purpose different applications of RBFs are used. To this end the numerical solutions are obtained without any mesh generation into the domain of the problems. The results of numerical experiments are compared with the existing results in illustrative examples to confirm the accuracy and efficiency of the presented scheme. Also the norm of the residual functions are obtained to show the convergence of the method.