An Iterative Scheme for Solving Arbitrary-Order Nonlinear Volterra Integro-Differential Equations Involving Delay

This paper introduces an iterative-based numerical scheme for solving nonlinear fractional-order Volterra integro-differential equations involving delay. Additionally, we provide sufficient conditions for the existence and uniqueness of the solution. The composite trapezoidal rule is applied to appr...

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Bibliographic Details
Published in:Iranian journal of science (Online) Vol. 47; no. 3; pp. 851 - 861
Main Authors: Ghosh, Bappa, Mohapatra, Jugal
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2023
Springer Nature B.V
Subjects:
Banach spaces
Calculus
Chemistry/Food Science
Derivatives
Differential equations
Earth Sciences
Engineering
Exact solutions
Integrals
Life Sciences
Materials Science
Mathematical functions
Mathematics
Operators (mathematics)
Physics
Research Paper
Volterra integral equations
65L03
L1 scheme
Error analysis
65R20
Volterra integro-differential equations
26A33
Trapezoidal rule
DGJ method
45D05
Delay
ISSN:2731-8095, 2731-8109
Online Access:Get full text
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Summary:This paper introduces an iterative-based numerical scheme for solving nonlinear fractional-order Volterra integro-differential equations involving delay. Additionally, we provide sufficient conditions for the existence and uniqueness of the solution. The composite trapezoidal rule is applied to approximate the integral involved in the equation, followed by discretizing the Caputo fractional derivative operator of arbitrary order α ∈ ( 0 , 1 ) by using the classical L1 scheme. Further, the Daftardar-Gejji and Jafari method is employed to solve the implicit algebraic equation. The convergence analysis and error bounds of the proposed scheme are presented. It is shown that the approximate solution converges to the exact solution with order ( 2 - α ) . We illustrate the efficacy and applicability of the proposed method through a couple of examples.
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ISSN:2731-8095
2731-8109
DOI:10.1007/s40995-023-01446-2