we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

In the framework of the continuum approximation, localized modes in nonlinear lattices ~‘‘intrinsic localized modes’’ or ‘‘discrete breathers’’! are described by the nonlinear Schrödinger ~NLS! equation. We go beyond this approximation and analyze what kind of qualitatively new effects can be introduced by discreteness. Taking into account the higher-order linear and nonlinear dispersion terms ...

and Applied Analysis 3 In 2008, Gordji et al. 17 provided the solution as well as the stability of a mixed type cubic-quartic functional equation. We only mention here the papers 19, 32, 33 concerning the stability of the mixed type functional equations. In this paper, we deal with the following general cubic-quartic functional equation: f ( x ky ) f ( x − ky) k2(f(x y) f(x − y)) 2 ( 1 − k2 ) f...

As is well known, equations of degree up to 4 can be solved in radicals . The solutions can be obtained, apart from the usual arithmetic operations, by the extraction of roots. In the case of the quadratic equation, this has a very concrete meaning. Even if the coefficients are arbitrary complex numbers, the solutions can always be calculated by the extraction of roots from nonnegative real num...

In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.

We report existence of a qualitatively distinct class of spiral waves in the two-dimensional cubic-quintic complex Ginzburg-Landau equation. These are stable clusters of localized states rotating around a central vortex core emerging due to interference of the tails of the individual states involved. We also develop an asymptotic theory allowing calculation of the angular frequency and stabilit...