We present an explicit second-order-accurate Godunov finite difference method for the solution of the equations of solid mechanics in one, two, and three spatial dimensions. The solid mechanics equations are solved in nonconservation form, with the novel application of a diffusion-like correction to enforce the gauge condition that the deformation tensor be the gradient of a vector. Physically ...

Backscatter is the process of energy transfer from small to large scales in turbulence; it is crucially important in the inverse energy cascades of two-dimensional and quasigeostrophic turbulence, where the net transfer of energy is from small to large scales. A numerical scheme for stochastic backscatter in the two-dimensional and quasigeostrophic inverse kinetic energy cascades is developed a...

Wedescribe and test an easy-to-implement two-step high-order compact (2SHOC) scheme for the Laplacian operator and its implementation into an explicit finite-difference scheme for simulating the nonlinear Schrödinger equation (NLSE). Our method relies on a compact ‘double-differencing’ which is shown to be computationally equivalent to standard fourthorder non-compact schemes. Through numerical...

We describe and test an easy-to-implement two-step high-order compact (2SHOC) scheme for the Laplacian operator and its implementation into an explicit finite-difference scheme for simulating the nonlinear Schrödinger equation (NLSE). Our method relies on a compact ‘double-differencing’ which is shown to be computationally equivalent to standard fourth-order non-compact schemes. Through numeric...

Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...

flood routing has many applications in engineering projects and helps designers in understanding the flood flow characteristics in river flows. floods are taken unsteady flows that vary by time and location. equations governing unsteady flows in waterways are continuity and momentum equations which in case of one-dimensional flow the saint-venant hypothesis is considered. dynamic wave model as ...

To solve the heat equation on parallel computers, a high-order finite difference domain decomposition algorithm is discussed. In this procedure, interface values between subdomains are calculated by the classical explicit scheme, while interior values of sub-domains are determined by the famous forth-order compact scheme. The stability and convergence for this domain decomposition algorithm are...

A new 9-point sixth-order accurate compact finite-difference method for solving the Helmholtz equation in one and two dimensions, is developed and analyzed. This scheme is based on sixth-order approximation to the derivative calculated from the Helmholtz equation. A sixth-order accurate symmetrical representation for the Neumann boundary condition was also developed. The efficiency and accuracy...