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.
Highlights
Integral equations find their application in physical sciences, finance, etc
The results substantiate that Elzaki transform method is a compatible alternate approach to other analytic methods like Laplace transform method and simple in application once compared with methods Adomian Decomposition Method (ADM) and Method of Successive Approximation (MSA)
We shall provide the solution for domain 0 to 1 and for comparison purposes, semi-analytic methods (ADM and MSA with zero as initial guess) solutions, have been given
Summary
Integral equations find their application in physical sciences, finance, etc. Diffraction problems, water waves, scattering in quantum mechanics are often. Integro-differential as well as related system of equations contains at least one variable limit of integration. Extensive mathematical techniques are available for finding analytic (exact), approximate analytic as well as numerical solutions of integral equations. Volterra type integral equations have been earlier solved using numerous methods available by mathematicians. In this paper some new applications of Elzaki transform have been discussed to find analytic solution of linear Volterra type integral equations which include convolution type as well as system of equations. The problems selected for demonstrating Elzaki transform application are those which have not been solved earlier using said transformation method. The analytic solutions obtained after application of Elzaki transform have been compared with results obtained through famous semi-analytical methods i.e. ADM and MSA (which have been restricted to first four iterations). The results establish the accuracy and simplicity of Elzaki transform method and attest its compatibility with Laplace transform
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