Numerical Modeling of Peridynamic Richards’ Equation with Piecewise Smooth Initial Conditions Using Spectral Methods

A numerical method for efficient 3D inversions using Richards equation

Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Saturation or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysi...

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

Solving wave equation with spectral methods and nonreflecting boundary conditions

A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics (Y m l (θ, φ)) for the angular dependence and of Chebyshev polynomials Tn(x) for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius R at which boundary conditions are imposed....

A Note on the Numerical Solution of the Wave Equation With Piecewise Smooth Coefficients

The numerical solution of the initial value problem for the wave equation is considered for the case when the equation coefficients are piecewise smooth. This problem models linear wave propagation in a medium in which the properties of the medium change discontinuously at interfaces. Convergent difference approximations can be found that do not require the explicit specification of the boundar...

Spectral Reconstruction of Piecewise Smooth Functions