A novel semi-analytical approach for solving nonlinear Volterra integro-differential equations

Kyunghoon Kim and Bongsoo Jang

Applied Mathematics and Computation, 2015, vol. 263, issue C, 25-35

Abstract: In this work, we present an efficient semi-analytical method based on the Taylor series for solving nonlinear Volterra integro-differential equations, namely the differential transform method (DTM). The DTM provides a recursive relation for the coefficients of the Taylor series that is derived from the given equations. We provide a new recursive relation for the nonlinear Volterra integro-differential equations with complex nonlinear kernels. Since the DTM is based on the Taylor series, it is difficult to obtain accurate approximate solutions in a large domain. To overcome this difficulty, the standard DTM is applied in each subdomain, called the multistage differential transform method (MsDTM). We also present an convergence analysis for the proposed method. To demonstrate the efficiency of the proposed method, several numerical examples are performed and support the results in our analysis.

Keywords: Volterra integro-differential equation; Taylor series; Differential transform method; Gronwall inequality (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315004622
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:apmaco:v:263:y:2015:i:c:p:25-35

DOI: 10.1016/j.amc.2015.04.011

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().