On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-19
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
All the previous authors discussed the quadratic equation only with continuous kernels by different methods.
In this paper, we introduce a mixed nonlinear quadratic integral equation (MQNLIE) with singular kernel in a logarithmic form and Carleman type.
An existence and uniqueness of MQNLIE are discussed.
A quadrature method is applied to obtain a system of nonlinear integral equation (NLIE), and then the Toeplitz matrix method (TMM) and Nystrom method are used to have a nonlinear algebraic system (NLAS).
The Newton–Raphson method is applied to solve the obtained NLAS.
Some numerical examples are considered, and its estimated errors are computed, in each method, by using Maple 18 software.
American Psychological Association (APA)
Basseem, M.& Alalyani, Ahmad. 2020. On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1200725
Modern Language Association (MLA)
Basseem, M.& Alalyani, Ahmad. On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels. Mathematical Problems in Engineering No. 2020 (2020), pp.1-7.
https://search.emarefa.net/detail/BIM-1200725
American Medical Association (AMA)
Basseem, M.& Alalyani, Ahmad. On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1200725
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1200725