The Arithmetic Mean iterative methods for sovling dense linear systems arise from first kind linear Fredholm integral equations

In the previous studies, the effectiveness of the Arithmetic Mean (AM) iterative method and its variants for solving various scientific problems has been investigated. Consequently, in this paper, the implementation and performance one of the AM method variants i.e. Quarter-Sweep Arithmetic Mean (QSAM) method for solving dense linear system associated with the numerical solution of first kind linear Fredholm integral equations are considered. The details of the method are discussed. Some numerical analyses were also conducted to verify the efficiency of the method

An implementation of the 2-point block arithmetic mean iterative method for first kind linear fredholm integral equations

In recent decades, many researches involving Arithmetic Mean (AM) iterative methods for solving matrix equations that arise from various scientific problems have been conducted. In this paper, application of the 2-Point Block Arithmetic Mean (2-BLAM) method to solve first kind linear Fredholm integral equations with semi-smooth kernel is investigated. The formulation and implementation of the method are discussed. Furthermore, numerical results of the method on test problems are also included

Solving second kind linear Fredholm integral equations via quarter-sweep SOR iterative method

In this paper, we consider the numerical solutions of linear Fredholm integral equations of the second kind. The Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method is applied to solve linear systems generated from discretization of the second kind linear Fredholm integral equations using quadrature method. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical tests and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method

Solving second kind linear Fredholm integral equation via Quarter-Sweep SOR Iterative method

In this paper, we consider the numerical solutions of linear Fredholm integral equations of the second kind. The Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method is applied to solve linear systems generated from discretization of the second kind linear Fredholm integral equations using quadrature method. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical tests and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method

Computational methods based on complexity reduction approach for first kind linear Fredholm integral equations with semi-smooth kernel

The main aim of this paper is to investigate the performance a family of Gauss-Seidel (GS) iterative method consists of Full-Sweep Gauss-Seidel (FSGS), Half-Sweep Gauss-Seidel (HSGS) and Quarter-Sweep Gauss-Seidel (QSGS) methods in solving linear systems associated with the first kind linear Fredholm integral equations. The details of the proposed methods are explained. Some numerical analyses are given in order to verify the performance of the proposed methods

Half-Sweep Geometric Mean Iterative Method for the Repeated Simpson Solution of Second Kind Linear Fredholm Integral Equations

In previous studies, the effectiveness of the Half-Sweep Geometric Mean (HSGM) iterative method has been shown in solving first and second kind linear Fredholm integral equations using repeated trapezoidal (RT) discretization scheme. In this work, we investigate the efficiency of the HSGM method to solve dense linear system generated from the discretization of the second kind linear Fredholm integral equations by using repeated Simpson's ^ (RS1) scheme. The formulation and implementation ofthe proposed method are also presented. In addition, several numerical simulations and computational complexity analysis were also included to verify the efficiency of the proposed method

Computational solution of first order linear fredholm integro-differential equations by quarter sweep successive over relaxation method

In this paper the effectiveness of the Quarter-Sweep Successive Over Relaxation (QSSOR) iterative method has been examined corresponding to finite difference-composite trapezoidal discretization schemes in solving first order linear Fredholm integro-differential equations. The mathematical formulations of the standard or Full-Sweep Successive Over Relaxation (FSSOR) methods also presented. Analysis of computational complexities and calculation of percentages reduction in number of iterations and execution time are also given to demonstrate that the QSSOR is superior compared to the standard Successive Over Relaxation method. Several numerical experiments have been shown to support the statements

The quarter-Sweep Geometric Mean Method for Solving Second Kind Linear Fredholm Integral Equations

Solving large linear systems is a fundamental problem in large scale scientific and engineering computations. In this paper, the formulation and implementation of the Quarter-Sweep Geometric Mean (QSGM) iterative method for solving large dense nonsymmetric linear systems associated with numerical solution of second kind linear Fredholm integral equations are explained. Furthermore, an analysis of computational complexity and numerical results by solving test problems are also included to verify the performance of the method

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

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

Comparisons of Quadrature Schemes with Arithmetic Mean Iterative Method for Second Kind Linear Fredholm Integral Equations

In this paper, we investigate the applications of two different quadrature schemes that is repeated trapezoidal (RT) and repeated modified trapezoidal (RMT) schemes via Arithmetic Mean iterative method to solve second kind linear Fredholm integral equations. Furthermore, the derivation and implementation of the proposed method are also included. Numerical tests and comparisons are given to illustrate the effectiveness of the proposed method