Cubic Hermite interpolation ensures continuity of derivatives between elements, so as well as providing an excellent representation of a smooth function, it also accurately models its gradients. Another attractive feature of this interpolation is that because each node is shared by neighbouring elements, a mesh of cubic Hermite elements has no more unknowns than a mesh of quadratic Lagrange ele...

A collective variable approach is used to map domains of existence for (3+1)-dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and ...

in this study we produced a new method for solving regular dierential equations with step size h and taylor series. this method analyzes a regular dierential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coecients and cubic and second- level equations.

The Fourier transforms of the products of two respectively three solutions of the free Schrödinger equation in one space dimension are estimated in mixed and, in the first case, weighted L norms. Inserted into an appropriate variant of the Fourier restriction norm method, these estimates serve to prove local well-posedness of the Cauchy problem for the cubic nonlinear Schrödinger (NLS) equation...

Abstract In this paper, we unify the system of functional equations defining a multi-quadratic–cubic mapping to single equation. Applying fixed point theorem, study generalized Hyers–Ulam stability mappings. As result, investigate hyperstability mappings in some senses.

Won{Gil Park [Won{Gil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the Hyers{Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadraticfunctional equation in 2{Banach spaces. One can easily see that all results of this paper are incorrect.Hence the control functions in all theorems of this paper are not correct. In this paper, we correctthes...

Any function relating several variables for which admissible scale transformations are specified is assumed to satisfy a functional equation that requires admissible transformations of the independent variables to effect only admissible transformations of the dependent variable. When there are not any dimensional constants that, in effect, cancel out the admissible transformations of the indepe...