Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method-Reference-Cited by-同舟云学术

Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method

Published:2019-02-03 Issue: Volume:2019 Page:1-10
ISSN:1687-9120
Container-title:Advances in Mathematical Physics
language:en
Short-container-title:Advances in Mathematical Physics

Author:

Ali Mohamed R.¹^ORCID,Mousa Mohamed M.¹²^ORCID,Ma Wen-Xiu³⁴⁵⁶^ORCID

Affiliation:

1. Department of Mathematics, Benha Faculty of Engineering, Benha University, Benha, Egypt

2. Department of Mathematics, College of Sciences and Human Studies at Howtat Sudair, Majmaah University, Al–Majmaah 11952, Saudi Arabia

3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

4. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China

6. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Abstract

We present a new numerical technique to discover a new solution of Singular Nonlinear Volterra Integral Equations (SNVIE). The considered technique utilizes the Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet method (HOBW) to solve the weakly SNVIE including Abel’s equations. We acquire the HOBW implementation matrix of the integration to derive the procedure of solving these kind integral equations. The explained technique is delineated with two numerical cases to demonstrate the benefit of the technique used by us. At last, the exchange uncovers the way that the strategy utilized here is basic in usage.

Funder

Majmaah University

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

Link

http://downloads.hindawi.com/journals/amp/2019/1705651.pdf

Reference25 articles.

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2. Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

3. Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations