Hyperbolic differential-difference equations with nonlocal potentials

Optimized Difference Schemes for Multidimensional Hyperbolic Partial Differential Equations

In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy) that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Semilinear Nonlocal Differential Equations with Delay Terms

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...

Impulsive Functional-differential Equations with Nonlocal Conditions

Numerical ‎S‎olution of Two-Dimensional Hyperbolic Equations with Nonlocal Integral Conditions Using Radial Basis Functions‎

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...