Two-dimensional wavelets scheme for numerical solutions of linear and nonlinear Volterra integro-differential equations

S. Behera and S. Saha Ray

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 198, issue C, 332-358

Abstract: In this article, an effective approach has been proposed to obtain the approximate solutions of linear and nonlinear two-dimensional Volterra integro-differential equations. First, the two-dimensional wavelets are introduced, and using it the operational matrices of integration, differentiation, and product have been constructed. Then, by utilizing the properties and matrices of wavelets along with the collocation point, the matrix form of Volterra integro-differential equations has been derived. This approach reduces the two-dimensional linear and nonlinear Volterra integro-differential equations into the system of linear and nonlinear algebraic equations respectively. The convergence analysis and error analysis have been extensively studied by the help of two-dimensional wavelets approximation. Some illustrative examples are examined to clarify the accuracy and effectiveness of the proposed scheme. The graphical representations obtained by two proposed wavelets have been plotted to justify the applicability and validity of the method.

Keywords: Two-dimensional Volterra integro-differential equation; Legendre wavelet; Bernoulli wavelet; Operational matrix; Collocation point (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475422000726
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:198:y:2022:i:c:p:332-358

DOI: 10.1016/j.matcom.2022.02.018

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().