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Bernstein Collocation Method for Solving High-Order Singular Differential–Difference Equations
The purpose of this article is to present an efficient numerical approach based on Bernstein polynomials for solving high-order linear singular...
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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 parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation
In this paper, a numerical method is presented to solve a nonlinear weakly singular time-fractional partial integro–differential equation with Caputo...
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Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel
In this paper, we propose an efficient numerical algorithm for the solution of fourth-order time fractional partial integro-differential equation...
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A Novel Fitted Three Term Method for the Numerical Treatment of Singularly Perturbed Differential–Difference Equations
An exponentially fitted method is proposed on uniform mesh for the numerical treatment of a boundary-value problem for the singularly perturbed...
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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 a Boundary Value Problem for a System of Differential–Difference Equations of Retarded Type
AbstractWe consider a control system described by a system of differential equations of retarded type with variable matrix coefficients and several...
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A Novel Fitted Method for a Class of Singularly Perturbed Differential-Difference Equations with Small Delay Exhibiting Twin Layer or Oscillatory Behaviour
AbstractA new exponentially fitted three term method is developed for the numerical treatment of a class of linear second order singularly perturbed...
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On the summability and convergence of formal solutions of linear q-difference-differential equations with constant coefficients
We consider the Cauchy problem for homogeneous linear q -difference-differential equations with constant coefficients. We characterise convergent, k -su...
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Spectral Solutions of Specific Singular Differential Equations Using A Unified Spectral Galerkin-Collocation Algorithm
This paper presents a novel numerical approach to addressing three types of high-order singular boundary value problems. We introduce and consider...
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A Deep Learning Neural Network Framework for Solving Singular Nonlinear Ordinary Differential Equations
This paper presents a deep learning feedforward neural network framework as a numerical tool to approximate the solutions to singular nonlinear...
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A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition
A class of singularly perturbed parabolic partial differential equations with a large delay and an integral boundary condition is studied. The...
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Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts
In this paper, exponentially fitted finite difference methods are presented for singularly perturbed one-dimensional parabolic partial differential...
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On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations
A family of singularly perturbed q -difference-differential equations under the action of a small complex perturbation parameter is studied. The...
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To the Theory of Singular Integral Equations of Non-Classical Type on a Segment of a Line
AbstractSingular integral operators with piecewise continuous matrix coefficients defined on segments of the real axis in weighted Lebesgue and...
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On Singular Points of Linear Differential-Algebraic Equations with Perturbations in the Form of Integral Operators
AbstractThe paper consideres linear systems of ordinary differential equations of arbitrary order with a matrix identically degenerate in the domain...
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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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On the Solvability of Boundary Value Problems for an Abstract Singular Equations on a Finite Interval
AbstractSufficient conditions for the unique solvability of boundary value problems for a number of abstract singular equations that are formulated...
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On Systems of Integro-Differential and Integral Equations with Identically Singular Matrix Multiplying the Principal Part
AbstractWe consider linear homogeneous systems of integro-differential and integral equations with Volterra and Fredholm matrix kernels with zero...
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Singular solutions for space-time fractional equations in a bounded domain
This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space...
