In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE)
on a finite but large spatial domain x∈[0, L], x= x (x, y, z) and t∈[0, T] are considered. Also in …

Cutting-Edge Techniques to Better Analyze and Predict Complex Physical Phenomena
Geometric Modeling and Mesh Generation from Scanned Images shows how to integrate …

The main goal of this chapter is to give the reader a (relatively) brief overview of operator-
splitting, augmented Lagrangian and ADMM methods and algorithms. Following a general …

Superdiffusion, characterized by a spreading rate t 1/α of the probability density function p (x,
t)= t− 1/α pt− 1/α x, 1, where t is time, may be modeled by space-fractional diffusion …

Multi-scale modeling plays an important role in understanding the structure and biological
functionalities of large biomolecular complexes. In this paper, we present an efficient …

This article develops a simple hybrid localized mesh-free method (LMM) for the numerical
modeling of new mixed subdiffusion and wave-diffusion equation with multi-term time …

In this paper, a new alternating direction implicit (ADI) method is introduced to solve
potential driven geometric flow PDEs for biomolecular surface generation. For such PDEs …

Abstract [eng] Analytical solutions to the fractional Riccati equation are considered in this
paper. Solutions to fractional differential equations are expressed in the form of fractional …

We will treat variational models that use Euler's elastica and related higher order derivatives
as regularizers. These models normally lead to higher order partial differential equations …

In this work, we investigate both the analytical and numerical studies of the dynamical model
comprising of three species systems. We analyze the linear stability of stationary solutions in …