Elayaraja Aruchunan

Application of Quarter-Sweep Iteration for First Order Linear Fredholm Integro-Differential Equations

The main core of this paper is to analyze the application of the quarter-sweep iterative concept on finite difference and composite trapezoidal schemes with Gauss-Seidel iterative method to solve first order linear Fredholm integro-differential equations. The formulation and implementation of the Full-, Half- and Quarter-Sweep Gauss-Seidel methods namely FSGS, HSGS and QSGS respectively are also presented for performance comparison. Furthermore, computational complexity and percentage reduction analysis are also included and integrated with several numerical simulations. Based on numerical results, findings show the proposed QSGS method with the corresponding discretization schemes is superior compared to FSGS and HSGS iterative methods.

Solving first kind linear Fredholm integral equations with semi-smooth kernel using 2-point half-sweep block arithmetic mean method

This paper investigates the application of the 2-Point Half-Sweep Block Arithmetic Mean (2-HSBLAM) iterative method with first order composite closed Newton-Cotes quadrature scheme for solving first kind linear Fredholm integral equations. The formulation and implementation of the method are presented. In addition, numerical results of test problems are also included to verify the performance of the method compared to existing Arithmetic Mean (AM) and 2-Point Full-Sweep Block Arithmetic Mean (2-FSBLAM) methods. From the numerical results, it is noticeable that the 2-HSBLAM method is superior than AM and 2-FSBLAM methods in terms of computational time.

Numerical performance of AOR methods in solving first order composite closed Newton-Cotes quadrature algebraic equations

In this paper, the application of the Accelerated Over-Relaxation (AOR) iterative method is extended to solve first order composite closed Newton-Cotes quadrature (1-CCNC) algebraic equations arising from second kind linear Fredholm integral equations. The formulation and implementation of the method are also discussed. In addition, numerical results by solving several test problems are included and compared with the conventional iterative methods.

Performance Analysis of Half-Sweep Successive Over-Relaxation Iterative Method for Solving Four-Point Composite Closed Newton-Cotes System

The theory and application of integral equations is an important subject within applied mathematics. Consequently, the main aim of this research paper is to investigate the performance of a variant of Successive Over-Relaxation iterative method i.e. Half-Sweep Successive Over-Relaxation (HSSOR) for solving four-point composite closed Newton-Cotes quadrature (4- CCNC) system that generated from linear Fredholm integral equations of the second kind. The numerical results from the simulations of the tested methods are presented.

Performance Analysis of 2-Point Explicit Group (2-EG) Method for Solving Second-Order Composite Closed Newton-Cotes Quadrature System

In this paper, the effectiveness of 2-Point Explicit Group (2-EG) iterative method with second-order composite closed Newton-Cotes (2-CCNC) quadrature scheme for solving second kind linear Fredholm integral equations is investigated. The formulation and implementation of the proposed method are presented. In addition, computational complexity analysis and numerical results of test examples are also included to verify the performance of the proposed method.

Preconditioned Jacobi-type iterative methods for solving Fredholm integral equations of the second kind

In this paper, performance analysis of the preconditioned Jacobi-type iterative methods for solving linear system arise from Fredholm integral equations of the second kind is investigated. The formulation and implementation of the proposed methods are presented. Also, numerical results are included in order to verify the performance of the methods.

A comparative study of iterative methods for solving first kind Fredholm integral equations with the semi-smooth kernel

The main aim of this paper is to investigate the performance of two iterative methods i.e. Gauss-Seidel (GS) and 2-Point Explicit Group (2-EG) in solving dense linear system associated with the numerical solution of first kind linear Fredholm integral equations. The formulation and implementation of the both methods are presented. In addition, some numerical results are also included to verify the effectiveness of the tested methods.

Valuing option on the maximum of two assets using improving modified Gauss-Seidel method

This paper presents the numerical solution for the option on the maximum of two assets using Improving Modified Gauss-Seidel (IMGS) iterative method. Actually, this option can be governed by two-dimensional Black-Scholes partial differential equation (PDE). The Crank-Nicolson scheme is applied to discretize the Black-Scholes PDE in order to derive a linear system. Then, the IMGS iterative method is formulated to solve the linear system. Numerical experiments involving Gauss-Seidel (GS) and Modified Gauss-Seidel (MGS) iterative methods are implemented as control methods to test the computational efficiency of the IMGS iterative method.

Numerical performance of half-sweep SOR method for solving second order composite closed Newton-Cotes system

In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.