COURSE DESCRIPTION The course is an introduction to the study of partial differential equations (PDEs) using functional analysis and energy methods. Questions of existence, uniqueness and regularity for weak solutions to linear elliptic and parabolic PDEs will be emphasized. Various nonlinear PDEs will also be studied, using a variety of different approaches, like variational and monotonicity m...

We show that matrix Q × Q Self-dual type S-integrable Partial Differential Equations (PDEs) possess a family of lower-dimensional reductions represented by the matrix Q × n 0 Q quasilinear first order PDEs solved in [29] by the method of characteristics. In turn, these PDEs admit two types of available particular solutions: (a) explicit solutions and (b) solutions described implicitly by a syst...

image restoration has been an active research area. dierent formulations are eective in high qualityrecovery. partial dierential equations (pdes) have become an important tool in image processingand analysis. one of the earliest models based on pdes is perona-malik model that is a kindof anisotropic diusion (andi) lter. anisotropic diusion lter has become a valuable tool indierent elds...

Abstract In this research paper, the authors aim to establish a novel algorithm in finite difference method (FDM). The idea is proposed mesh generation process, process generate random grids. FDM over randomly generated grid enables fast convergence and improves accuracy of solution for given problem; it also enhances quality precision by minimizing error. involves uniform grids, which are comm...

Numerical solution of PDEs is rich and active field of modern applied mathematics. The steady growth of the subject is stimulated by everincreasing demands from the natural sciences, engineering and economics to provide accurate and reliable approximations to mathematical models involving partial differential equations (PDEs) whose exact solutions are either too complicated to determine in clos...

With the advent of virtual machine (VM)-based platforms for parallel computing, it is now possible to execute parallel discrete event simulations (PDES) over multiple virtual machines, in contrast to executing in native mode directly over hardware as is traditionally done over the past decades. While mature VM-based parallel systems now offer new, compelling benefits such as serviceability, dyn...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

Partial differential equations (PDEs) are the conventional tool for the description of timeand space-dependent physical phenomena. Vector PDEs arise from the physical analysis of multidimensional (MD) systems in terms of potential and flux quantities. Expressing the resulting coupled PDEs in vector form facilitates the direct formulation of boundary and interface conditions in their physical co...

The second messenger cGMP is involved in several physiological functions such as smooth muscle relaxation and inhibition of platelet aggregation. Besides cGMP synthesis, hydrolysis of cGMP by cyclic nucleotide phosphodiesterases (PDEs) determines the shape of cGMP signals. Eleven PDE families are known differing in regulation and cAMP/cGMP specificity. PDEs are homodimers; each monomer being co...

The current paper outlines a new algorithm, which is used to determine the exact solutions of ODEs and the similarity transformations of PDEs whose the invariant groups are known. Three groups of formulations (named by HAMAD Formulations) are presented: (I) Formulations for the exact solutions of ODE. (II) Formulations for similarity transformations of PDEs contains two independent variables. (...