A new code for Volterra integral equations based on natural Runge-Kutta methods

A. Abdi; G. Hojjati; Zdzislaw Jackiewicz; H. Mahdi

doi:10.1016/j.apnum.2019.03.016

A new code for Volterra integral equations based on natural Runge-Kutta methods

A. Abdi, G. Hojjati, Zdzislaw Jackiewicz, H. Mahdi

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We describe some issues related to the development of a new code for numerical solution of systems of Volterra integral equations of the second kind. This code is based on A- and V ₀ -stable natural Volterra Runge-Kutta method of order p=4 implemented in a variable stepsize environment. This method was derived by Conte et al. (2014) [13]. The numerical experiments on many equations and systems of equations illustrate that the code achieves the expected order of accuracy, and confirm its efficiency and robustness.

Original language	English (US)
Pages (from-to)	35-50
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	143
DOIs	https://doi.org/10.1016/j.apnum.2019.03.016
State	Published - Sep 2019

Keywords

A- and V -stability
Implementation issues
Natural Volterra Runge-Kutta methods
Volterra integral equation of the second kind

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1016/j.apnum.2019.03.016

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title = "A new code for Volterra integral equations based on natural Runge-Kutta methods",

abstract = " We describe some issues related to the development of a new code for numerical solution of systems of Volterra integral equations of the second kind. This code is based on A- and V 0 -stable natural Volterra Runge-Kutta method of order p=4 implemented in a variable stepsize environment. This method was derived by Conte et al. (2014) [13]. The numerical experiments on many equations and systems of equations illustrate that the code achieves the expected order of accuracy, and confirm its efficiency and robustness. ",

keywords = "A- and V -stability, Implementation issues, Natural Volterra Runge-Kutta methods, Volterra integral equation of the second kind",

author = "A. Abdi and G. Hojjati and Zdzislaw Jackiewicz and H. Mahdi",

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AU - Abdi, A.

AU - Hojjati, G.

AU - Jackiewicz, Zdzislaw

AU - Mahdi, H.

PY - 2019/9

Y1 - 2019/9

N2 - We describe some issues related to the development of a new code for numerical solution of systems of Volterra integral equations of the second kind. This code is based on A- and V 0 -stable natural Volterra Runge-Kutta method of order p=4 implemented in a variable stepsize environment. This method was derived by Conte et al. (2014) [13]. The numerical experiments on many equations and systems of equations illustrate that the code achieves the expected order of accuracy, and confirm its efficiency and robustness.

AB - We describe some issues related to the development of a new code for numerical solution of systems of Volterra integral equations of the second kind. This code is based on A- and V 0 -stable natural Volterra Runge-Kutta method of order p=4 implemented in a variable stepsize environment. This method was derived by Conte et al. (2014) [13]. The numerical experiments on many equations and systems of equations illustrate that the code achieves the expected order of accuracy, and confirm its efficiency and robustness.

KW - A- and V -stability

KW - Implementation issues

KW - Natural Volterra Runge-Kutta methods

KW - Volterra integral equation of the second kind

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EP - 50

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

A new code for Volterra integral equations based on natural Runge-Kutta methods

Abstract

Keywords

ASJC Scopus subject areas

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