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An integral discretization scheme on a graded mesh for a fractional differential equation with integral boundary conditions
In this paper, a fractional differential equation with integral conditions is studied. The fractional differential equation is transformed into an...
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On One Integral Representation of Solutions of Polyharmonic Equation
AbstractIn the paper, an elementary solution of polyharmonic equation is determined and, with the help of it, an integral representation of solutions...
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Mixed Problem with Integral Condition for a Loaded Third Order Pseudoparabolic Equation
We consider a nonlocal problem with an integral condition for a loaded third order pseudoparabolic equation in a rectangular domain. We prove the...
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Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures
AbstractWe consider the differential and integral statements of problems of acoustic scattering by three-dimensional bounded transparent structures...
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On a Non-Linear Differential-Integral Equation
AbstractExact analytical solutions to a non-linear differential-integral equation that appears in a stochastic optimal control problem are given. The...
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On the integral solution of hyperbolic Kepler’s equation
In a recent paper of Philcox, Goodman and Slepian, the solution of the elliptic Kepler’s equation is given as a quotient of two contour integrals...
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Generalized Boundary Integral Equation Method for Boundary Value Problems of Two-D Isotropic Lattice Laplacian
A generalized boundary integral equation method for boundary value problems of two-dimensional isotropic lattice Laplacian is proposed in this paper....
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Fredholm integral equation in composed-cone metric spaces
The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples...
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Scattering integral equation formulation for intravascular inclusion biosensing
A dielectric waveguide, inserted into blood vessels, supports its basic mode that is being scattered by a near-field intravascular inclusion. A...
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Integral Transform Method for Solving Inhomogeneous Heat Equation with Mixed Boundary Conditions
The inhomogeneous heat equation for a semi-infinite cylindrical solid body with mixed boundary conditions of the first and second kinds on the...
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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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Euler Integral Symmetries and the Asymptotics of the Monodromy for the Heun Equation
Euler integral transform connects monodromy matrices of the Heun equation with different sets of parameters. In this paper, this fact is used to...
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Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations
An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels....
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Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function
This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the...
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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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Fredholm Integral Equation of the Second Kind with Degenerate Kernel
In this section, we will describe the method of solution of the integral equation (2.1) with degenerate kernel k(x, t) given by equation (2.4) by...
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Existence of Solutions to a Conformally Invariant Integral Equation Involving Poisson-Type Kernels
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation...
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Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space
AbstractWe study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced....
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An Iterative Scheme for Solving a Lippmann–Schwinger Nonlinear Integral Equation by the Galerkin Method
AbstractThe purpose of this study is to solve a nonlinear integral equation describing the propagation of electromagnetic waves in a body located in...
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Inverse Source Problem for the Subdiffusion Equation on a Metric Star Graph with Integral Overdetermination Condition
AbstractIn this article, it is investigated the inverse source problem for the subdiffusion equation on the metric star graph in Sobolev space with...