Results 51 to 60 of about 2,472 (168)

Deep learning schemes for parabolic nonlocal integro-differential equations

Partial Differential Equations and Applications, 2022
AbstractIn this paper we consider the numerical approximation of nonlocal integro differential parabolic equations via neural networks. These equations appear in many recent applications, including finance, biology and others, and have been recently studied in great generality starting from the work of Caffarelli and Silvestre by Lius and Lius (Comm ...
openaire   +3 more sources

On Stability of a Third Order of Accuracy Difference Scheme for Hyperbolic Nonlocal BVP with Self-Adjoint Operator

Abstract and Applied Analysis, 2013
A third order of accuracy absolutely stable difference schemes is presented for nonlocal boundary value hyperbolic problem of the differential equations in a Hilbert space H with self-adjoint positive definite operator A. Stability estimates for solution
Allaberen Ashyralyev, Ozgur Yildirim
doaj   +1 more source

FDM for Elliptic Equations with Bitsadze-Samarskii-Dirichlet Conditions

Abstract and Applied Analysis, 2012
A numerical method is proposed for solving nonlocal boundary value problem for the multidimensional elliptic partial differential equation with the Bitsadze-Samarskii-Dirichlet condition.
Allaberen Ashyralyev, Fatma Songul Ozesenli Tetikoglu   +1 more
doaj   +1 more source

On the nonlinear impulsive Ψ–Hilfer fractional differential equations

Mathematical Modelling and Analysis, 2020
In this paper, we consider the nonlinear Ψ-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions.
Kishor D. Kucche, Jyoti P. Kharade, J. Vanterler da C. Sousa   +2 more
doaj   +1 more source

Nonlocal symmetries and recursion operators: Partial differential and differential–difference equations

Journal of Mathematical Analysis and Applications, 2005
After brief explanation of the basic definitions and notions connected with nonlocal symmetries of DEs the authors present a systematic method to derive the nonlocal symmetries for PDEs with two independent variables and show that KdV \(\frac{\partial u}{\partial t}=u\frac{\partial u}{\partial x}+\frac{\partial ^3 u}{\partial x^3}\) and Burgers \(\frac{
Sahadevan, R., Khousalya, S., Devi, L. Nalini   +2 more
openaire   +1 more source

On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

Abstract and Applied Analysis, 2012
We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established.
Allaberen Ashyralyev, Okan Gercek
doaj   +1 more source

On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem [PDF]

International Journal of Stochastic Analysis, 1998
In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the ...
openaire   +2 more sources

Global solutions for abstract functional differential equations with nonlocal conditions

Electronic Journal of Qualitative Theory of Differential Equations, 2009
In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.
Eduardo Hernandez, Sueli M. Tanaka Aki
doaj   +1 more source

To the Solution of Loaded Differential Equations with Nonlocal Conditions

The Bulletin of Irkutsk State University. Series Mathematics
We investigate a system of linear ordinary differential equations containing point and integral loadings with nonlocal boundary conditions. Boundary conditions include integral and point values of the unknown function. An essential feature of the problem is that the kernels of the integral terms in the differential equations depend only on the ...
openaire   +3 more sources

Point force in a plane in the context of fractional nonlocal elasticity

Archives of Mechanics
Solutions to the point load problems for elastic solids have different applications in geomechanics, contact mechanics, tribology as well as in modeling of lattice defects in crystals.
Y. Povstenko, T. Kyrylych, A. Yatsko
doaj   +1 more source