in this paper, we consider orthogonal stability of mixed type additive and cubic functional equation of the form $$f(2x+y)+f(2x-y)-f(4x)=2f (x+y)+2f(x-y)-8f(2x) +10f(x)-2f(-x),$$ with $xbot y$, where $bot$  is orthogonality in the sense of ratz.

ABSTRACT An accurate closed-form solution for the quintic Duffing equation is obtained using a cubication method. In this method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude. The replacement of the origi...

A construction is given for a planar rational Pythagorean hodograph spiral which interpolates any two-point G Hermite data that a spiral can match. When the curvature at one of the points is zero, the construction gives the unique interpolant that is the involute of a rational Pythagorean hodograph curve of the form cubic over linear. Otherwise, the spiral comprises an involute of a Tschirnhaus...

We consider the transmission problem for second-order diierential equations with unbounded interfaces. The spaces B and B are used to prove the limiting absorption principle for the steady-state problem and to establish the resolvent estimate at low frequencies for the steady-state operator. These are then applied in showing the validity of the limiting amplitude principle for such an operator....

A method to compute the scattering solutions of a spinless Salpeter equation ~or a Schrödinger equation! with a central interaction is presented. This method relies on the three-dimensional Fourier grid Hamiltonian method used to compute bound states. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the scattering solution at the same ...

We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schr odinger equation, we present the results of numerical experiments in which the integration in time is p...