Higher Order Compact Implicit Schemes for the Wave Equation

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

Several studies have presented compact fourth order accurate finite difference approximation for the Helmholtz equation in two or three dimensions. Several of these formulae allow for the wave number k to be variable. Other papers have extended this further to include variable coefficients within the Laplacian which models non-homogeneous materials in electromagnetism. Later papers considered m...

Higher Order Numerical Schemes for Paraxial Approximations of the Wave Equation

In a previous work, Collino and Joly 9] have constructed new 3D paraxial approximations that are compatible with the use of splitting methods without loss of accuracy. We present here new higher order numerical schemes to solve these equations in an heterogeneous medium. The dispersion eeects observed by using classical second-order schemes can be considerably attenuated, even with a very few n...

Upwind schemes for the wave equation in second-order form

We develop new high-order accurate upwind schemes for the wave equation in second-order form. These schemes are developed directly for the equations in second-order form, as opposed to transforming the equations to a first-order hyperbolic system. The schemes are based on the solution to a local Riemann-type problem that uses d’Alembert’s exact solution. We construct conservative finite differe...

Implicit Schemes for the Lattice Boltzmann Equation

Implicit RBF Meshless Method for the Solution of Two-dimensional Variable Order Fractional Cable Equation

In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...