in this paper, the numerical solution methods of one- particale, one – dimensional time- independentschrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function v(x). these methods included the fem(finite element method), cooly, numerov and others. here we considered the numerov method inmore details...

A computationally efficient approximate analytical solution based on the classic solution for diffraction about a semi-infinite breakwater, is developed to assess the wave energy shadow down-wave of a single row array of overtopping type wave energy converters approximated as partially transmitting breakwater segments. The approximations associated with the solution are mitigated by a compariso...

Free and self-excited vibrations of conservative oscillators with polynomial nonlinearity are considered. Mathematical model of the system is a second-order differential equation with a nonlinearity of polynomial type, whose terms are of integer and/or noninteger order. For the case when only one nonlinear term exists, the exact analytical solution of the differential equation is determined as ...

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index struct...

When polymeric liquids undergo large-amplitude shearing oscillations, the shear stress responds as a Fourier series, the higher harmonics of which are caused by fluid nonlinearity. Previous work on large-amplitude oscillatory shear flow has produced analytical solutions for the first few harmonics of a Fourier series for the shear stress response (none beyond the fifth) or for the normal stress...

in this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (srlw) equation and the (3+1)-dimensional shallow water wave equations. solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions the physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. note t...

because of fluctuation in leg tension, pitch motion is very effective fatigue and life safety of leg elements in tension leg structures (tlss). in this paper an exact solution for pitch vibration of a tls interacting with ocean wave is presented. the legs of tlp are considered as elastic springs. the flow is assumed to be irrotational and single-valued velocity potentials are defined. the effec...