TITLE:
Some New Applications of Elzaki Transform for Solution of Linear Volterra Type Integral Equations
AUTHORS:
Saad Sharjeel, Mushtaq Ahmed Khan Barakzai
KEYWORDS:
Elzaki Transform, Linear Volterra Integral Equation, Adomian Decomposition Method, Method of Successive Approximation, Laplace Elzaki Duality (LED)
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.8,
August
23,
2019
ABSTRACT: Volterra type integral equations have diverse applications in scientific and other fields. Modelling physical phenomena by employing integral equations is not a new concept. Similarly, extensive research is underway to find accurate and efficient solution methods for integral equations. Some of noteworthy methods include Adomian Decomposition Method (ADM), Variational Iteration Method (VIM), Method of Successive Approximation (MSA), Galerkin method, Laplace transform method, etc. This research is focused on demonstrating Elzaki transform application for solution of linear Volterra integral equations which include convolution type equations as well as one system of equations. The selected problems are available in literature and have been solved using various analytical, semi-analytical and numerical techniques. Results obtained after application of Elzaki transform have been compared with solutions obtained through other prominent semi-analytic methods i.e. ADM and MSA (limited to first four iterations). The results substantiate that Elzaki transform method is not only a compatible alternate approach to other analytic methods like Laplace transform method but also simple in application once compared with methods ADM and MSA.