Comparison of the results obtained by Iman transform with Laplace transform

Abstract

Many processes in the real world are characterised by principles which are defined in the form of expressions involving rates of change. Mathematically, rates are derivatives and expressions are equations so we have differential equations. Differential equations play an important role for modelling many problems in different scientific fields. Sometimes, the calculations to solve these equations can be very complex and ultimately frustrating. For this reason, many integral transform methods were proposed by researchers. However, integral transform methods can give consistent solutions to many complex problems and have many application areas such as physics, mechanics, engineering, astronomy. In this work, two integral transforms, Iman transform and the well-known Laplace transform were studied comparatively to facilitate the solution of linear ordinary differential equations with constant coefficients. Applications of these two transforms show that these integral transform methods are closely related to each other.

Keywords

• iman transform
• laplace transform
• integral transform
• differential equations.