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A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
oundary integral equations Nystrom discretization Singular integrals Nearly singular integrals Fast solvers Laplace equation Stokes equation Navier equation Fast multipole method Fast Fourier transform
2015/7/14
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...
Numerical Solution of Generalized Abel’s Integral Equation by Variational Iteration Method
Variational Iteration Method Singular Integral Equation Abel’s Kernel
2013/1/30
In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approxi...
Numerical Solution of the Fredholme-Volterra Integral Equation by the Sinc Function
Fredholme-Volterra Integral Equation Sinc Function Collocation Method
2013/1/30
In this paper, we use the Sinc Function to solve the Fredholme-Volterra Integral Equations. By using collocation method we estimate a solution for Fredholme-Volterra Integral Equations. Finally conver...
Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix
Abel Inversion Bernstein Polynomials Almost Bernstein Operational Matrix Of Integration Noise Resistance
2013/1/30
A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier pr...
The expansions approach for solving Cauchy integral equation of the first kind
Cauchy integral equation Chebyshev polynomials
2010/9/27
In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determine...
Modified Neumann series for solving Fredholm integral equation
Perturbation Method Fredholm integral equation
2010/9/13
In this paper we present a modification to Neumann series method for solving Fredholm integral equation. We create a perturbation in left side of Fredholm integral equation and we show the decrement o...
On a Certain Volterra-Fredholm Type Integral Equation
Volterra-Fredholm type integral equation Banach fixed point theorem integral inequality Bielecki type norm existence and uniqueness continuous dependence
2010/1/22
The aim of this paper is to study the existence, uniqueness and other properties of solutions of a certain Volterra-Fredholm type integral equation. The main tools employed in the analysis are based o...
A Numerical Method in Terms of the Third Derivative for a Delay Integral Equation from Biomathematics
Delay Integral Equation Successive approximations Perturbed trapezoidal quadrature rule
2008/7/3
This paper presents a numerical method for approximating the positive, bounded and smooth solution of a delay integral equation which occurs in the study of the spread of epidemics. We use the cubic s...
Positive and Nontrivial Solutions for the Urysohn Integral Equation
Urysohn integral equation positive solutions eigenvalues
2007/12/12
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficien...
While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion ...
Mixed Type of Integral Equation with Potential Kernel
Fredholm integral equations Potential kernel Legendre and Jacobi polynomials Weber-Sonien integral
2010/2/25
This paper presents the solution of an integral equation of a mixed type in three-dimensions in the space L2 (W) \times C[0,T], where T < \infty, and W is the domain of integration with respect to pos...
Classification of Solutions for an Integral Equation
Classification of Solutions Integral Equation
2018/4/20
Let n be a positive integer and let 0 < ® < n: Consider theintegral equationu(x) =ZRn1jx ¡ yjn¡® u(y)(n+®)=(n¡®)dy: (0.1) We prove that every positive regular soluti...