<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, an effectual and new modification in Laplace Adomian decomposition method based on Bernstein polynomials is proposed to find the solution of nonlinear Volterra integral and integro-differential equations. The performance and capability of the proposed idea is endorsed by comparing the exact and approximate solutions for three different examples on Volterra integral, integro-differential equations of the first and second kinds. The results shown through tables and figures demonstrate the accuracy of our method. It is concluded here that the non orthogonal polynomials can also be used for Laplace Adomian decomposition method. In addition, convergence analysis of the modified technique is also presented.</p></abstract>

In this paper, an effectual and new modification in Laplace Adomian decomposition method based on Bernstein polynomials is proposed to find the solution of nonlinear Volterra integral and integro-differential equations. The performance and capability of the proposed idea is endorsed by comparing the exact and approximate solutions for three different examples on Volterra integral, integro-differential equations of the first and second kinds. The results shown through tables and figures demonstrate the accuracy of our method. It is concluded here that the non orthogonal polynomials can also be used for Laplace Adomian decomposition method. In addition, convergence analysis of the modified technique is also presented.

Solutions of Volterra integral and integro-differential equations using modified Laplace Adomian decomposition method

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, an effectual and new modification in Laplace Adomian decomposition method based on Bernstein polynomials is proposed to find the solution of...

Solutions of Volterra integral and integro-differential equations using modified Laplace Adomian decomposition method

Published Online: Jun 22, 2019

Page range: 5 - 18

DOI: https://doi.org/10.2478/jamsi-2019-0001

Keywords
Laplace transformation, Adomian decomposition method, modified Laplace Adomian decomposition method, Bernstein polynomials, Volterra integral and integro-differential equations

© 2019 Faculty of Natural Sciences, University of Saint Cyril and Metodius, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Solutions of Volterra integral and integro-differential equations using modified Laplace Adomian decomposition method

Published Online: Jun 22, 2019

Page range: 5 - 18

DOI: https://doi.org/10.2478/jamsi-2019-0001

KeywordsLaplace transformation, Adomian decomposition method, modified Laplace Adomian decomposition method, Bernstein polynomials, Volterra integral and integro-differential equations

© 2019 Faculty of Natural Sciences, University of Saint Cyril and Metodius, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Laplace transformation, Adomian decomposition method, modified Laplace Adomian decomposition method, Bernstein polynomials, Volterra integral and integro-differential equations