A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

We extend a recently introduced method for numerically solving partial differential equations on implicit surfaces (Bertalmı́o, Cheng, Osher, and Sapiro 2001) to fourth order PDEs including the CahnHilliard equation and a lubrication model for curved surfaces. By representing a surface in N as the level set of a smooth function, φ we compute the PDE using only finite differences on a standard Ca...

The complementary differential operator is devised to decouple two coupled partial differential equations with variable coefficients. This complementary operator transforms two coupled partial differential equations into a pair of uncoupled equations either of (i) fourth order, (ii) third order, or (iii) second order. The conditions for the existence of linearly dependent solutions for two coup...

This article concerns mathematical image denoising methods incorporating fourth-order partial differential equations (PDEs). We introduce and analyze piecewise planarity conditions (PPCs) with which unconstrained fourth-order variational models in continuum converge to a piecewise planar image. It has been observed that fourth-order variational models holding PPCs can restore better images than...

A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in i...