scholarly journals Half-Sweep Arithmetic Mean method with composite trapezoidal scheme for solving linear Fredholm integral equations

2011 ◽  
Vol 217 (12) ◽  
pp. 5442-5448 ◽  
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Jumat Sulaiman
Keyword(s):  
Integral Equations ◽  
Arithmetic Mean ◽  
Fredholm Integral Equations

Performance analysis of Arithmetic Mean method for solving composite 6-point closed Newton–Cotes quadrature algebraic equation

2019 ◽  
Vol 12 (04) ◽  
pp. 1950061
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Emanuele Galligani ◽  
Majid Khan Majahar Ali ◽  
Jumat Sulaiman ◽  
Ramoshweu Solomon Lebelo
Keyword(s):  
Performance Analysis ◽  
Linear System ◽  
Iterative Method ◽  
Integral Equations ◽  
Algebraic Equation ◽  
Arithmetic Mean ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Dense Linear System

The main focus of the paper is to study the performance of Arithmetic Mean (AM) iterative method in solving large and nonsingular dense linear system arising from the composite 6-point closed Newton–Cotes quadrature (6-CCNC) approximation of inhomogeneous linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. Some numerical results are also presented.

scholarly journals Half-Sweep Arithmetic Mean Method with High-Order Newton-Cotes Quadrature Schemes to Solve Linear Second Kind Fredholm Equations

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Jumat Sulaiman
Keyword(s):  
Linear Systems ◽  
Integral Equations ◽  
Arithmetic Mean ◽  
High Order ◽  
Fredholm Integral Equations ◽  
Fredholm Equations ◽  
Discretization Schemes

The main purpose of this paper is to examine the effectiveness of the Half-Sweep Arithmetic Mean (HSAM) method in solving the dense linear systems generated from the discretization of the linear Fredholm integral equations of the second kind. In addition, the applications of the various orders of closed Newton-Cotes quadrature discretization schemes will be investigate in order to form linear systems. Furthermore, the basic formulation and implementation for the proposed method are also presented. Some illustrative examples are given to point out the efficiency of the proposed method.

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