A challenging difficulty in solving the radial Dirac eigenvalue problem numerically is the presence of spurious (unphysical) eigenvalues among the correct ones that are neither related to mathematical interpretations nor to physical explanations. Many attempts have been made and several numerical methods have been applied to solve the problem using finite element method (FEM), finite difference...

A Computational Analysis of the Black-Scholes Equations by Yifan Wang This paper explores the most decorated option pricing model in recent history of the financial industry: the Black-Scholes Equation. We will first study the framework of the Black-Scholes Equation in detail by introducing its object of evaluation, distinguished assumptions, and deduction of the Black-Scholes partial different...

Computational modelling has received significant attention in the research community over the past few decades due to its pronounced contribution in better understanding of the nature, as well as in the development of advanced technologies. The modelling of more and more complex transport physical systems helps the community to address important issues, like identification of environmental prob...

In this paper, we derive a highly accurate numerical method for the solution of one-dimensional wave equation with Neumann boundary conditions. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method and the time variable is discretized by using various classical finite difference schemes. The numerical results show t...

In this article, finite difference method (FDM) is used to solve sixth-order derivatives of differential equations in buckling analysis of nanoplates due to coupled surface energy and non-local elasticity theories. The uniform temperature change is used to study thermal effect. The small scale and surface energy effects are added into the governing equations using Eringen’s non-local elasticity...

In this article, finite difference method (FDM) is used to solve sixth-order derivatives of differential equations in buckling analysis of nanoplates due to coupled surface energy and non-local elasticity theories. The uniform temperature change is used to study thermal effect. The small scale and surface energy effects are added into the governing equations using Eringen’s non-local elasticity...

We study effects of finite height and surrounding material on photonic crystal slabs of oneand two-dimensional photonic crystals with a pseudo-spectral method and finite difference time domain simulation methods. The band gap is shown to be strongly modified by the boundary material. As an application we suggest reflection and guiding of light by patterning the material on top/below the slab.

A technique to incorporate directivity in the Pseudospectral time-domain method (PSTD) for auralization purposes is presented. The Pseudospectral time-domain method is a numerical method for solving the wave equation that requires only two spatial points per wavelength, making it more efficient compared to other wave based methods. The effect of source directivity as well as the head-related di...

In this article, finite difference method (FDM) is used to study the size-dependent free vibration characteristics of rectangular nanoplates considering the surface stress effects. To include the surface effects in the equations, Gurtin-Murdoch continuum elasticity approach has been employed. The effects of surface properties including the surface elasticity, surface residual stress and surface...

Taking the axial heat conduction of wax deposition layer into account, a two-dimensional heat transfer model of calculating the temperature profile inside wax deposition layer was deduced and established based on the energy balance equation, the finite difference method was used to solve this model, and the influence of axial heat conduction on the distribution law of temperature profile inside...