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Reflecting Function and a Generalization of the Notion of First Integral
AbstractThe relationships between the notion of generalized integral and the notions of reflecting function and Poincaré map (period map) for...
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Uniform Aproximations of Solutions to a Strongly Singular Integral Equation of the First Kind
AbstractThe article is devoted to uniform approximations of the solution of a periodic strongly singular integral equation of the first kind. We note...
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A Method for Solving the Fredholm Integral Equation of the First Kind
The paper considers a numerical method for solving the Fredholm integral equation of the first kind. The essence of the method is to replace the...
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Nontrivial Solutions for a First-order Impulsive Integral Boundary Value Problem on Time Scales
In this paper we use topological degree to study the solvability for a first-order impulsive integral boundary value problem on time scales. We first...
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Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method
AbstractA numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of...
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On the Solvability of Fredholm Boundary Integral Equations of the First Kind for the Three-Dimensional Transmission Problem on the Spectrum
AbstractThe paper considers two weakly singular Fredholm boundary integral equations of the first kind to each of which the three-dimensional...
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Numerical solution of the two-dimensional first kind Fredholm integral equations using a regularized collocation method
In this study, we present an advanced numerical model for solving the 2D first kind Fredholm integral equations, which are well known to be ill-posed...
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Well-Posedness of a Problem of Solving Some Classes of Integral Equations of the First Kind
AbstractThis article is devoted to the study of the well-posedness of the problem of solving some classes of integral and integro-differential...
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Integral Equations
Fredholm and Volterra integral equations are considered. Fredholm alternative is formulated. Problems are devoted to solving of integral equations of...
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Block-by-block method for solving non-linear Volterra integral equation of the first kind
In this paper, we focus on the numerical solution of the non-linear Volterra integral equation of the first kind. We start by converting its form to...
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Definite Integral
The definite integral is defined and examples of definite integration by substitution are given. Integration of even, odd and periodic functions is...
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On Numerical Solution of a First Kind Integral Equation with a Weak Singularity in the Kernel on a Closed Surface
AbstractA direct method (self-regularization method) for the numerical solution of a weakly singular integral equation of the first kind on a closed...
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Abel Integral Equations
The simplest form of the Abel integral equation is given by $$\int _{0}^{x}\frac{\phi...
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Integral Representations and Integral Identities
Working in the complex plane, in §1.1 we prove versions of the classical Cauchy-Pompeiu integral representation formula, Morera’s Theorem, the...
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The Integral
In this chapter we extend the theory of the integral to functions of several variables defined on subsets of...