In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and col...

We present and demonstrate a method for blind separation and bearing estimation of broadband traveling waves, impinging on a sensor array with dimensions smaller than the shortest wavelength in the sources. By sensing spatial and temporal gradients of the received signal, the problem of separating mixtures of time-delayed sources reduces to that of separating instantaneous mixtures of the gradi...

In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting numerical is high order accurate in space time. As novel scheme handles two derivatives, operator for both derivatives has be defined. This results extended system matrix sc...

In this paper, a fractional degree cubic spline scheme is proposed and analyzed for order with the multi-term Riemann–Liouvile (R–L) derivatives. For integral differential equations, we handle continuity equations attain system of linear algebraic by using matrix method based on piecewise test functions. The to solve initial value problems approximate solution equation approximation Reimann–Lio...

We consider Einstein’s equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data, classical solutions break down in finite time. The key mathematical result is a new theorem on the breakdown of solutions of systems of balance laws. We also show ...

The one-dimensional Schrödinger equation is considered when the potential is real valued, integrable, and has a finite first moment. The small-energy asymptotics of the logarithmic spatial derivative of the Jost solutions are established. Some consequences of these asymptotics are presented such as the small-energy limits of the scattering coefficients and a simplified characterization of the s...

Phase unwrapping is probably the most challenging step in the phase retrieval process in phase-shifting and spatial-carrier interferometry. Likewise, phase unwrapping is required in 3D-shape profiling and deflectometry. In this paper, we present a novel phase retrieval method that completely sidesteps the phase unwrapping process, significantly eliminating the guessing in phase reconstruction a...

Peridynamics (PD) is a nonlocal continuum theory based on integro-differential equations without spatial derivatives. The elongation fracture criterion is implicitly incorporated in the PD theory, and fracture is a natural outcome of the simulation. On the other hand, a new fracture criterion based on the crack opening displacement combined with peridynamic (PD-COD) is proposed. When the relati...

phenylazo and benzothiazolylazo derivatives of trifluoroacetylacetone andhexafluoroacetylacetone have been synthesized and characterized. analytical and spectral datarevealed the existence of phenylazo derivatives in the intramolecularly hydrogen-bonded ketohydrazoneform while the benzothiazolylazo derivatives in the azo-enol form. the monobasicbidentate coordination of the phenylazo derivative...

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by . 0 = ∂ ∂ + ∂ ∂ x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised s...