Solving One-Dimensional Heat and Wave Equations Via Gupta Integral Transform

Abstract

The partial differential equations which represent the one-dimensional heat and wave equations are generally solved by the techniques: exact, approximate, and purely numerical. Since the application of numerical method becomes more complex, computationally intensive, or needs complicated symbolic computations, there is a need to seek the help of integral transform methods for solving the partial differential equations representing the one-dimensional heat and wave equations. Heat and wave equations are some of the well-known partial differential equations applicable in basic sciences, and engineering. Integral transform methods provide effective ways for solving a variety of problems arising in basic sciences and engineering. The Gupta transform is a new integral transform applied for solving differential equations like other integral transforms. In this study, Gupta transform is introduced for solving the one-dimensional heat and wave equations formulated in terms of partial differential equations. The concept and properties of the Gupta transform are also discussed.