Partial Differential Equations (PDEs) have become an important tool in image processing and analysis. A PDE mode for image zooming is introduced in this paper. This model exploits a higher order nonlinear partial differential equation. The resulted nonlinear equation is solved by an explicit finite difference schemes. Numerical results on real digital images are given to show effectiveness and ...

We derive a class of globally convergent and quadratically converging algorithms for a system of nonlinear equations g(u) = 0, where g is a sufficiently smooth homeomorphism. Particular attention is directed to key parameters which control the iteration. Several examples are given that have successful in solving the coupled nonlinear PDEs which arise in semiconductor device modelling. AMS subje...

The aim of this paper is to sketch two examples of simple queuing networks that possess nonlinear diffusion approximations. These approximations are obtained by considering hydrodynamic limits for the corresponding interacting particle systems obeying various exclusion rules. Asymptotic analysis of the approximating nonlinear pdes is also provided.

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which ...

This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equations (PDEs). In the paper we present a general framework for constructing high order interior penalty discontinuous Galerkin (IP-DG) methods for approximating viscosity solutions of these fully nonlinear PDEs. In order...

An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The special case of a general that produces pre-symplectic operator non-gradient adjoint-symmetry. These formulas are illustrated by several examples linear PDEs integrable nonlinear PDEs. Addit...

Many problems in finance can be posed in terms of an optimal stochastic control. Some well-known examples include transaction cost/uncertain volatility models [17, 2, 25], passport options [1, 26], unequal borrowing/lending costs in option pricing [9], risk control in reinsurance [23], optimal withdrawals in variable annuities[13], optimal execution of trades [20, 19], and asset allocation [28,...

The workshop discussed the numerical solution of linear and nonlinear eigenvalue problems for partial differential equations. It included the theoretical analysis the development of new (adaptive) methods, the iterative solution of the algebraic problems as well as the application in many areas of science and engineering. Mathematics Subject Classification (2000): 65N25, 65F15, 15A18. Introduct...

In this paper, we explore more applications of the hyperbolic function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations (PDES), to special discrete nonlinear equations. Some exact travelling wave solution of the discrete sine-Gordon equation are obtained in terms of hyperbolic fun...

As a significant strengthening of properties of earlier algebras of generalized functions, here are presented classes of such algebras which can deal with dense singularities. In fact, the cardinal of the set of singular points can be larger than that of the nonsingular points. This large class of singularities allows the solution of large classes of smooth nonlinear PDEs. This in certain ways ...