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Integro-Differential Equation with a Sum-Difference Kernels and Power Nonlinearity
AbstractSharp a priori estimates are obtained for solutions to a nonlinear Volterra-type integro-differential equation with a sum-difference kernel...
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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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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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Initial-Boundary Value Problem for a Multidimensional Integro-Differential Equation of Hyperbolic Type and a Difference Method for its Numerical Implementation
AbstractIn this paper, we consider an initial-boundary value problem for a multidimensional integro-differential equation of hyperbolic type. For an...
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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 Compact Difference Scheme on Graded Meshes for the Nonlinear Fractional Integro-differential Equation with Non-smooth Solutions
In this paper, a compact finite difference scheme for the nonlinear fractional integro-differential equation with weak singularity at the initial...
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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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Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect
We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We...
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Asymptotic Regimes of an Integro-Difference Equation with Discontinuous Kernel
This paper is concerned with an integral equation that models discrete time dynamics of a population in a patchy landscape. The patches in the domain...
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A Robust Finite Difference Method for the Solutions of Singularly Perturbed Fredholm Integro-Differential Equations
This article deals with a fitted mesh finite difference method for solving a singularly perturbed Fredholm integro-differential equation. At first,...
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Rotational Symmetry and Rotating Waves in Planar Integro-Difference Equations
Mathematical models often possess symmetries, either because of actual symmetries of the situation being modelled, or as approximations. It is well...
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An iterative difference scheme for solving arbitrary order nonlinear Volterra integro-differential population growth model
This paper develops and analyzes an efficient iterative-based finite difference scheme to find the approximate solution of the nonlinear time...
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Wave speed and critical patch size for integro-difference equations with a strong Allee effect
Simplified conditions are given for the existence and positivity of wave speed for an integro-difference equation with a strong Allee effect and an...
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A spectral collocation matrix method for solving linear Fredholm integro-differential–difference equations
In this study, a spectral collocation matrix method has been introduced to solve the linear Fredholm integro differential–difference equation...
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Asymptotic Behavior of Solutions of a Complete Second-Order Integro-Differential Equation
In this paper, we study a complete second-order integro-differential operator equation in a Hilbert space. The difference-type kernel of an integral...
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Analysis of BDF2 finite difference method for fourth-order integro-differential equation
In this work, the stability and error analysis are presented for fully discrete solutions of the fourth-order differential equation with the...
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A Novel Uniform Numerical Approach to Solve a Singularly Perturbed Volterra Integro-Differential Equation
AbstractIn this paper, the initial value problem for the second order singularly perturbed Volterra integro-differential equation is considered. To...
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Numerical Solution of the Cauchy Problem for a Second-Order Integro-Differential Equation
AbstractIn a finite-dimensional Hilbert space, we consider the Cauchy problem for a second-order integro-differential evolution equation with memory...
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A Crank–Nicolson-type finite-difference scheme and its algorithm implementation for a nonlinear partial integro-differential equation arising from viscoelasticity
A Crank–Nicolson-type finite-difference scheme is proposed and analyzed for a nonlinear partial integro-differential equation arising from...
