Abstract
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 1/3(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.
Highlights
Integral equations of various types play an important role in many fields of science and engineering
Integral equations are encountered in numerous applications in many fields including continuum mechanics, potential theory, geophysics, electricity and magnetism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control systems, communication theory, mathematical economics, population genetics, queuing theory, medicine, mathematical problems of radiative equilibrium, particle transport problems of astrophysics and reactor theory, acoustics, fluid mechanics, steady state heat conduction, fracture mechanics, and radiative heat transfer problems [25]
In order to measure the computational complexity of the FSGM and Half-Sweep Geometric Mean (HSGM) methods, an estimation amount of the computational work required for iterative methods have been conducted
Summary
Integral equations of various types play an important role in many fields of science and engineering. Linear Fredholm integral equations of the second kind are considered. Second kind linear integral equations of Fredholm type in the generic form can be defined as follows. Further studies to verify the effectiveness of the HSGM method with Crank-Nicolson finite difference [2] and quadrature [13, 14] schemes to solve water quality model and linear Fredholm integral equations respectively have been carried out. In this paper, the application of the HSGM method using the half-sweep quadrature approximation equation based on repeated. Scheme for solving second kind linear Fredholm integral equations is examined.
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