Applications on Laplace Transforms, Elzaki Transforms and Sumdu Transforms Using Initial and Boundary Conditions

Abstract

The Laplace transform, Elzaki transform, and Sumudu transform methods are used in this paper to solve initial value problems directly without having to convert them to ordinary differential equations. One of the three methods can be used to solve initial value problems using these transformation techniques. By applying the relevant transform to the governing equation and initial conditions, initial value problems can be addressed using the Laplace, Elzaki, and Sumudu transform methods. By doing this, problems can be solved without having to convert them to ODE form. Transforming the initial value problems directly leads to solutions being obtained in one of the three proposed approaches: Laplace, Elzaki, or Sumudu. The added complexity of transforming problems to ODEs before using transforms to find solutions is avoided by this reformulation.