New homotopy analysis transform algorithm to solve volterra integral equation

By Sunil Kumar, Jagdev Singh, Devendra Kumar, S. Kapoor. 2014

58 citations recorded by the source corpus.

Abstract The main aim of the present work is to propose a new and simple algorithm for Volterra integral equation arising in demography, the study of viscoelastic materials, and in insurance mathematics through the renewal equation by using homotopy analysis transform method. The homotopy analysis transform method is an innovative adjustment in Laplace transform algorithm and makes the calculation much simpler. The solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. The beauty of the paper is coupling of two techniques. Finally, two numerical examples are given to show the accuracy and stability of this method.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/af25057001f6399e990f224dd512d13eae96b896

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Eisa Zarei
2. Hasan Barzegar Kelishami
3. Samad Noeiaghdam

In Modeling and Simulation

1. Eisa Zarei
2. Hasan Barzegar Kelishami
3. Samad Noeiaghdam

In Numerical Analysis

1. Eisa Zarei
2. Hasan Barzegar Kelishami
3. Samad Noeiaghdam

Citations in the corpus

• Homotopy analysis transform method for solving Abel’s integral equations of the first kind (2016, methodology): “In recent years, many authors have paid attention to studying the solutions of linear and nonlinear differential and integral equations using homotopy analysis method combined with the Laplace transform method [8,9].”