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The adjoint double layer potential on smooth surfaces in \(\mathbb {R}^3\) and the Neumann problem
We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for...
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Application of Bernstein polynomials for solving Fredholm integro-differential-difference equations
In this paper, the Bernstein polynomials method is proposed for the numerical solution of Fredholm integro-differential-difference equation with...
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On Approximate Solution of Certain Equations
In this paper, we consider problems of discrete approximation of special integral operators with the Calderon–Zygmund kernel. We introduce discrete...
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Operators and Equations: Discrete and Continuous
We consider discrete pseudo-differential equations with elliptic symbols and the corresponding discrete boundary-value problems in special canonical...
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Extrapolated regularization of nearly singular integrals on surfaces
We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or...
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A spectral method for a weakly singular Volterra integro-differential equation with pantograph delay
In this paper, a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay, which contains a weakly...
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Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis
In this paper, the approximate solutions for two different type of two-dimensional nonlinear integral equations: two-dimensional nonlinear...
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An adaptive kernel-split quadrature method for parameter-dependent layer potentials
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular...
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Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology
Numerical simulations with rigid particles, drops, or vesicles constitute some examples that involve 3D objects with spherical topology. When the...
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Zeta correction: a new approach to constructing corrected trapezoidal quadrature rules for singular integral operators
A high-order accurate quadrature rule for the discretization of boundary integral equations (BIEs) on closed smooth contours in the plane is...
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An accelerated, high-order accurate direct solver for the Lippmann–Schwinger equation for acoustic scattering in the plane
An efficient direct solver for solving the Lippmann–Schwinger integral equation modeling acoustic scattering in the plane is presented. For a problem...
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High-order corrected trapezoidal rules for a class of singular integrals
We present a family of high-order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity....
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Analysis and Fast Approximation of a Steady-State Spatially-Dependent Distributed-order Space-Fractional Diffusion Equation
We prove the wellposedness of a distributed-order space-fractional diffusion equation with variably distribution and its support, which could...
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A fast solver for elastic scattering from axisymmetric objects by boundary integral equations
Fast and high-order accurate algorithms for three-dimensional elastic scattering are of great importance when modeling physical phenomena in...
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A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels
We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure...
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Nyström method for BEM of the heat equation with moving boundaries
A direct boundary integral equation method for the heat equation based on Nyström discretization is proposed and analyzed. For problems with moving...
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Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis
This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev...
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Spectral method for multidimensional Volterra integral equation with regular kernel
This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We...
