Solving the Axisymmetric Dirichlet Potential using the One-Variable Hankel Transform of the I-Function | Original Article

ABSTRACT:

The study presents a novel and efficient approach to solving the axisymmetric Dirichlet potential problem by employing the one-variable Hankel transform of the I-function. The Dirichlet potential problem, a fundamental concept in mathematical physics, arises in various fields including electromagnetism, fluid dynamics, and heat conduction. Traditional solutions often involve complex mathematical manipulations and extensive computational efforts. In this research, we leverage the powerful tool of the one-variable Hankel transform applied to the Ifunction, a special function in mathematical analysis. By transforming the governing equations into the Hankel domain, we simplify the problem significantly, reducing it to a manageable form. The transformed equations are solved analytically, leading to explicit solutions for the axisymmetric Dirichlet potential. The efficiency and accuracy of the proposed method are demonstrated through comprehensive numerical simulations and comparisons with existing solutions. Using the Hankel transform of an Ifunction in one variable, we have solved the famous Axisymmetric Dirichlet problem for a half-space in this study. When dealing with cylindrical coordinates and boundary value issues, the Hankel transform is a powerful tool. We have solved the Axisymmetric Dirichlet problem in a half space defined by the following equations