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Decomposition and conformal map** techniques for the quadrature of nearly singular integrals
Gauss–Legendre quadrature, Clenshaw–Curtis quadrature and the trapezoid rule are powerful tools for numerical integration of analytic functions. For...
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A block-by-block strategy for fractional systems of nonlinear weakly singular integro-differential equations
This paper concentrates on providing a new approach to arrive at approximate solution of a fractional nonlinear system of weakly singular...
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Numerical approach for weakly singular equation with nonlinear delay
Solving weakly singular equations has wide applications in engineering and science. The delay term makes it difficult for most existing solvers to...
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A high-order compact ADI finite difference scheme on uniform meshes for a weakly singular integro-differential equation in three space dimensions
We propose a new compact alternating direction implicit (ADI) finite difference scheme on uniform meshes for a weakly singular integro-differential...
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An Efficient Spectral-Galerkin Method for Second Kind Weakly Singular VIEs with Highly Oscillatory Kernels
In this paper, we construct an efficient spectral Galerkin method to deal with the classical second kind linear VIEs with weakly singular and highly...
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An hp-version of the discontinuous Galerkin method for fractional integro-differential equations with weakly singular kernels
This paper suggests an hp -discontinuous Galerkin approach for the fractional integro-differential equations with weakly singular kernels. The key...
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Inevitable monokineticity of strongly singular alignment
We prove that certain types of measure-valued map**s are monokinetic i.e. the distribution of velocity is concentrated in a Dirac mass. These...
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Corrected trapezoidal rule for near-singular integrals in axi-symmetric Stokes flow
The paper presents a method to evaluate near-singular boundary integrals in axi-symmetric interfacial Stokes flow for target points close to but not...
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Form-Boundedness and SDEs with Singular Drift
We survey and refine recent results on weak and strong well-posedness of stochastic differential equations with singular drift satisfying some...
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Computational study based on the Laplace transform and local discontinuous Galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels
The aim of this paper is to implement the high-order local discontinuous Galerkin method (LDGM) for solving partial integro-differential equations...
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Weakly Canceling Operators and Singular Integrals
AbstractWe suggest an elementary harmonic analysis approach to canceling and weakly canceling differential operators, which allows us to extend...
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A Solution to a Boundary-Value Problem for Integro-Differential Equations with Weakly Singular Kernels
A linear boundary-value problem for a system of integro-differential equations with weakly singular kernels is considered. Questions of the unique...
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A fast collocation method for solving the weakly singular fractional integro-differential equation
In the present paper, we propose a spectral collocation method based on Pell polynomials to obtain the solution of a variable-order fractional...
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Doubly Singular Elliptic Equations Involving a Gradient Term: Symmetry and Monotonicity
Let u be a positive singular solution to boundary semilinear elliptic problems with a gradient term and a possibly singular nonlinearity. We prove...
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Singular Value Functions
This chapter is a detailed study of properties of the generalized singular value function of a...
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Asymptotic Stability for Singular Diffusions
In the present chapter, asymptotic stability conditions for diffusions with linear drift and Lipschitz diffusion coefficients are presented. Although...
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On a wavelet-based numerical method for linear and nonlinear fractional Volterra integro-differential equations with weakly singular kernels
A wavelet-based technique has been used in this study to solve the linear and nonlinear fractional order Volterra integro-differential equations...
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Crank–Nicolson Schemes for Sub-Diffusion Equations with Nonsingular and Singular Source Terms in Time
In this work, two Crank–Nicolson schemes without corrections are developed for sub-diffusion equations. First, we propose a Crank–Nicolson scheme...
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Numerical Solution of a Weakly Singular Integral Equation by the Method of Orthogonal Polynomials in Various Function Classes
AbstractWe consider a singular integral equation with a logarithmic singularity that is used in the mathematical model of the scattering of...