pμ dx /h̄, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of ...

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

In this paper a parallel algorithm is presented for the numerical solution of the heat equation with derivative boundary conditions. The parallel algorithm is developed by approximating the second-order spatial partial derivative by third-order finite-difference approximations and a matrix exponential function by a rational approximation having distinct real poles. Problems are solved using the...

System of panel models are popular models in applied sciences and the question of spatial errors has created the recent demand for spatial system estimation of panel models. Therefore we propose new diagnostic methods to explore if the spatial component will change significantly the outcome of non-spatial estimates of seemingly unrelated regression (SUR) systems. We apply a local sensitivity ap...

 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...

In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on $L2$-$1_\sigma$ formula and exponential-sum-approximation technique. The evaluation method can achieve accuracy further reduce computational cost acting memory for VO derivative. This algorithm applied construct relevant temporal spatial fourth-order s...

This paper applies the multiquadric (MQ) as a spatial approximation scheme for solving the nonlinear Burgers' equation. For comparison purposes, a low order explicit nite diierence approximation of the time derivative is employed. By decreasing the time step of the computation , it is shown that the major numerical error is from the time integration instead of the MQ spatial approximation. The ...