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Method of separation of variables and exact solution of time fractional nonlinear partial differential and differential-difference equations
In this article we consider a certain class of time fractional nonlinear partial differential equations as well as partial differential-difference...
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Differential-Difference Equations with Optimal Parameters
AbstractThe paper considers difference schemes with optimal parameters for solving Maxwell’s equations. Using Laguerre transforms, the numerical...
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On entire solutions of Fermat type difference and kth order partial differential difference equations in several complex variables
In this paper, we investigate the existence and specific form of finite order transcendental entire solutions of certain equations including a...
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Existence of meromorphic solutions of systems of partial differential–difference equations
In this paper, we show a sufficient condition on the existence of admissible meromorphic solutions of system of complex partial delay differential...
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Linear Moment Partial Differential Equations
Introduced in the 2010 article (Funkcial Ekvac 53:411–434, 2010) by W. Balser and M. Yoshino in order to present a new tool to study the classical...
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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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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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Numerical solution of time dependent nonlinear partial differential equations using a novel block method coupled with compact finite difference schemes
In this paper, we have developed a novel three step second derivative block method and coupled it with fourth order standard compact finite...
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A Mingled Tau-Finite Difference Method for Stochastic First-Order Partial Differential Equations
Herein, we offer a numerical spectral-FD solution to a one-dimensional linear first-order stochastic partial differential equation driven by...
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Partial Differential Equations An Introduction to Analytical and Numerical Methods
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two...
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Exact solution of time-fractional differential-difference equations: invariant subspace, partially invariant subspace, generalized separation of variables
We present how the invariant subspace method of differential equations can be extended to scalar and coupled fractional differential-difference...
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On Solvability of Parabolic Equations with Essentially Nonlinear Differential-Difference Operators
We consider the first mixed boundary value problem for a nonlinear differential-difference parabolic equation. We give some sufficient conditions for...
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Difference Approach to Solving Boundary Value Problems for Elliptic Partial Differential Equations in the Sense of Generalized Functions
AbstractAn approach is described for constructing homogeneous difference schemes using difference analogs of partial derivatives of regular...
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Entire solutions for some Fermat type functional equations concerning difference and partial differential in ℂ2
The main purpose of this paper is concerned with the existence and the forms of transcendental entire solutions of several Fermat type functional...
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Existence of the Solution to the Cauchy Problem for Nonlinear Stochastic Partial Differential-Difference Equations of Neutral Type
The authors consider the existence of the solution to the Cauchy problem in the class of nonlinear stochastic partial differential-difference...
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Partial Differential Equations and Applications Colloquium in Honor of Hamidou Touré, Ouagadougou, Burkina Faso, November 5–9, 2018
This volume convenes selected, peer-reviewed works presented at the Partial Differential Equations and Applications Colloquium in Honor of Prof....
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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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Partial Differential Equations
We first build a second difference block matrix corresponding to the Laplacian on the square. We use this Laplacian matrix with various enforced...
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On the Construction of a Variational Principle for a Certain Class of Differential-Difference Operator Equations
In this paper, we obtain necessary and sufficient conditions for the existence of variational principles for a given first-order...