Yang Transformation for Solving Transport and Poisson Equations

Abstract

Integral transforms have become powerful analytical tools for solving ordinary and partial differential equations arising in applied mathematics, physics, and engineering. In this paper, the Yang transform is employed to derive analytical solutions of the Transport and Poisson equations. General solution formulas are established for homogeneous and non-homogeneous Transport equations as well as for the Poisson equation under the prescribed initial and boundary conditions. The proposed approach transforms the governing partial differential equations into ordinary differential equations, leading to a simpler and more systematic solution procedure. Several illustrative examples are presented to verify the validity and effectiveness of the derived formulas. The obtained results demonstrate that the Yang transform provides an efficient and reliable analytical technique for solving these classes of partial differential equations and may be extended to other mathematical models encountered in applied sciences and engineering.