We consider the following two classes of second order boundary value problems for difference equation: Δ ( r i 1 Δ y i 1 ) b i y i + λ a i y i = 0 , 1 i n , y 0 τ y 1 = y n + 1 δ y n = 0 with δ , τ∈ [ 0 , 1 ] and Δ ( r i 1 Δ y i 1 ...
The Riemann problems are solved through an approximate solver in order to calculate a set of time-averaged fluxes needed in the scheme. The scheme is tested through numerical examples involving strong shocks. It is shown that the scheme offers the principle advantages of a second order Godunov ...
By applying the graded mesh-based fast L2- 1 σ formula and the ADI technique for the equivalent lower system of the original equation, we can derive a fast second-order ADI finite difference scheme for the high-dimensional fractional model with spatially variable coefficients (1). The ...
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We develop a robust solver for a second order mixed finite element splitting scheme for the Cahn–Hilliard equation. This work is an extension of our previous work in which we developed a robust solver for a first order mixed finite element splitting scheme for the Cahn–Hilliard equation. The...
The behaviour is compared of two solvers for the discrete equations arising from the discretization using Chebyshev collocation of a second-order linear partial differential equation on a square. The alternative solvers considered are a direct solver and an iterative solver based on preconditioning with...
A Multigrid Solver for the Helmholtz Equation on a Semiregular Grid on the Sphere A multigrid finite-difference solver is developed for the Helmholtz equation on the sphere. The finite-difference grid resolution is constant in the latitu... KP Bowman,H Jin - 《Monthly Weather Review》 被引量...
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Second-order nonlinear optical processes convert light from one wavelength to another and generate quantum entanglement. Creating chip-scale devices to efficiently control these interactions greatly increases the reach of photonics. Existing silicon-base
To model the second order nonlinear DD-LE equation, fix the values of m and n as: (4)m+n=2,m,n≥1.The Eq. (3) takes the form as: (5)d2dx2u(x−τ)+ρxddxu(x−τ)+g(u)=0,u(0)=α,du(0)dx=0.The singularity in the above equation appears single time at point x...