The Numerical Solution of Klein-Gorden Equation by Using Nonstandard Finite Difference

Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes

Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with spe...

Numerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods

numerical solution of klein-gordon equation by using the adomian's decomposition and variational iterative methods

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

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 ...

Finite Difference-Time Domain solution of Dirac equation and the Klein Paradox

The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein paradox: potential step barriers and linear potentials. No Klein paradox is observed.