Solving Wave Equation and Heat Equation by Rohit Transform (RT)

Abstract

The wave equation and the heat equation are widely known differential equations coming to light in engineering, basic and material sciences. The differential equations which represent the wave equation and the heat equation are usually solved by the exact technique or by the approximate technique or by the purely numerical technique. Since the implementation of these techniques is very complex, computationally vigorous, and requires elaborate computations, therefore, for finding the solutions of differential equations depicting the wave equation and the heat equation, there is a need to ask for integral transform techniques. Integral transform techniques render productive means for finding the solutions of problems coming to light in engineering, basic and material sciences. The Rohit transform (RT) is a new integral transformation put forward by the author Rohit Gupta recently in the year 2020 and has been utilized for finding the solutions of problems coming to light in engineering, basic and material sciences like other transform techniques. In this study, the RT is brought in for finding the solutions of the heat equation and the wave equation expressed in terms of differential equations which are generally partial in nature.