Fredholm–Volterra integral equation of the first kind and contact problem
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In this paper, under certain condition the Fredholm-Volterra integral equation of the first kind is solved. The existence. and uniqueness of the solution is considered. The Fredholm integral equation of the second kind is established from the work, and its solution is also obtained.
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The objective of this work is to study Fredholm integral equations to know its usefulness in reallife situations. The usefulness of Fredholm integral equations depend on the field of study.Fredholm integral equations seem to deal with unknown problems and find answers to thateffect. Fredholm integral equation is applied in many fields such as kinetic theory of gases,electricity and magnetism, medicine, mathematical problems of radioactive equilibrium. Theseare the essential scientific research in which integral equation sought to apply. The Fredholmlinear integral equation of the first and second kinds with separable kernels will be useful insolving unknown functions. The eigenvalue as well as the homogeneous equation will be vitalinterest in this work.
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Many of the problems in the real world that can be brought into a mathematical
model. One of the widely used is linear Fredholm integral equation of the
second kind. Fredholm integral equation of the second kind is a equation with unknown
function appears inside and outside the integral sign as well as the limits
of the integral form of a constant. There are various methods that can be used to
solve Fredholm integral equation. Method for solving integral equations can be either
analytic methods and numerical methods. Analytical methods that can be used
include Adomian decomposition method, the decomposition modification methods,
direct calculation method, the method of successive approximations, and the series
solution method will be discussed in this thesis. These methods provide different
algorithms, as well as providing completion in the form of exact solution.
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The Fredholm integral equation with a Green's function type of kernel has been transformed by Drukarev into an equivalent Volterra equation. It is now proven that the Neumann series solution of the Volterra equation yields the determinantal solution of the Fredholm equation. Thus, a Born approximation technique suffices to obtain the full Fredholm solution.
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Fredholm theory
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Fredholm theory
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This chapter discusses the approximate solution of the Fredholm factorization. Chapter Contents: 5.1 The integral equations in the α − plane 5.1.1 Introduction 5.1.2 Source pole αο with positive imaginary part 5.1.3 Analytical validation of a particular W-H equation 5.1.4 A property of the integral in the Fredholm equation 5.1.5 Numerical solution of the Fredholm equations 5.1.6 Analytic continuation outside the integration line 5.2 The integral equations in the w − plane 5.3 Additional considerations on the Fredholm equations 5.3.1 Presence of poles of the kernel in the warped region 5.3.2 The Fredholm factorization for particular matrices 5.3.3 The Fredholm equation relevant to a modified kernel Inspec keywords: Fredholm integral equations; computational electromagnetics Other keywords: computational electromagnetics; Fredholm factorization Subjects: Numerical approximation and analysis; Electric and magnetic fields; Integral equations (numerical analysis); Classical electromagnetism
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Fredholm theory
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