On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation

H. S. Mamba; M. Khumalo

doi:10.1155/2014/763160

On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation

H. S. Mamba, M. Khumalo

Mathematics and Applied Mathematics

University of Johannesburg

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

1 Citation (Scopus)

Abstract

We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results.

Original language	English
Article number	763160
Journal	Abstract and Applied Analysis
Volume	2014
DOIs	https://doi.org/10.1155/2014/763160
Publication status	Published - 2014

ASJC Scopus subject areas

Analysis
Applied Mathematics

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title = "On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation",

abstract = "We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results.",

author = "Mamba, {H. S.} and M. Khumalo",

note = "Publisher Copyright: {\textcopyright} 2014 H. S. Mamba and M. Khumalo.",

year = "2014",

doi = "10.1155/2014/763160",

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AU - Khumalo, M.

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Y1 - 2014

N2 - We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results.

AB - We consider the numerical solutions of a class of nonlinear (nonstandard) Volterra integral equation. We prove the existence and uniqueness of the one point collocation solutions and the solution by the repeated trapezoidal rule for the nonlinear Volterra integral equation. We analyze the convergence of the collocation methods and the repeated trapezoidal rule. Numerical experiments are used to illustrate theoretical results.

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DO - 10.1155/2014/763160

M3 - Article

AN - SCOPUS:84934913048

SN - 1085-3375

VL - 2014

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

M1 - 763160

ER -

On the Analysis of Numerical Methods for Nonstandard Volterra Integral Equation

Abstract

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