What is it about?
This investigation is concerned with the solutions of Volterra integral equations of second kind that have been determined by employing Optimal Homotopy Asymptotic method (OHAM). The existence and uniqueness of solutions are proved in this work. The convergence of the approximate solutions using the proposed method is investigated. Error’s estimation to the corresponding numerical scheme is also carried out.
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Why is it important?
Volterra integral equations have many applications such as human population forecasting, torsion of wire, control problems, propagation of nervous impulse and Abel’s problem. The Volterra integral equations are used to determine the energy, action and flow characteristics of a wave. These equations are also arise in many scientific fields such as the study of viscoelastic materials, spread of epidemic, and semi-conductor devices.
Perspectives
The obtained solutions are novel, and previous literature lacks such derivations. The reliability and accuracy of OHAM have been shown by comparison of our derived solutions with solutions obtained by other existing methods. The efficiency of the proposed numerical technique is exhibited through graphical illustrations, and results are drafted in tabular form for specific values of parameter to validate the numerical investigation.
Prof. Dr Saif Ullah
Government College University Lahore
Read the Original
This page is a summary of: Numerical Investigation of Volterra Integral Equations of Second Kind using Optimal Homotopy Asymptotic Method, Applied Mathematics and Computation, October 2022, Elsevier,
DOI: 10.1016/j.amc.2022.127304.
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