Solving 3D Helmholtz Equation Using Triple Laplace-Aboodh-Sumudu Transform

This paper introduces a novel integral transform, termed the triple Laplace-Aboodh-Sumudu transform (TLAST), by combining the Laplace transform, Aboodh transform, and Sumudu transform. The primary objective of this research is to utilize TLAST for solving the Helmholtz equation in three dimensions. The TLAST provides a powerful tool for transforming complex partial differential equations into algebraic equations, simplifying their solution. The paper presents the mathematical formulation of TLAST and demonstrates its application in solving the Helmholtz equation. By employing TLAST, the solution to the Helmholtz equation is obtained efficiently, highlighting the potential of this new integral transform in addressing various problems in science, engineering, and other fields. Keywords: Triple Laplace-Aboodh-Sumudu transform, Helmholtz equation, Integral transform, Laplace transform, Aboodh transform, Sumudu transform.