This paper develops a modification of the dressing method based on inhomogeneous linear integral equation with integral operator having nonempty kernel. Method allows one to construct the systems of multidimensional Partial Differential Equations (PDEs) having differential polynomial structure in any dimension n. Associated solution space is not full, although it is parametrized by certain numb...

We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to s...

Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit t...

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using Partial Differential Equations (PDEs). It combines a non-linear Fourth-ord...

Abstract This paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efficient implementations of discontinuous Galerkin (DG) method solving wide range nonlinear partial differential equations (PDEs). Although C++ interfaces are flexible and customizable, solid knowledge is necessary to make use this powerful tool. With work, easier user based on ...

in this paper, we investigate some problems which can be reduced to the goursat problem for afourth order equation. some results and theorems are given concerning the existence and uniqence for thesolution of the suggested problem.

The present paper deals with a toxin producing phytoplankton (TPP)-zooplankton interaction in spatial environment in thecontext of phytoplankton bloom. In the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. After that TPP-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both popu...

The classical Feynman–Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing representations for solutions of linear Kolmogorov PDEs. This opens the door derivation sampling based Monte Carlo approximation methods, which can be meshfree thereby stand chance to approximate PDEs without suffering from curse dimensionality. In this paper, we...

Boundary control for systems governed by partial differential equations (PDEs) is an important field with many practical and theoretical issues. The topic of boundary control of PDEs has been the subject of a considerable literature since the seminal works of J.-L. Lions in the 90s. In this paper, we consider the boundary control of systems represented by spatial discretizations of PDEs (i.e. s...

In this paper, we consider the numerical approximation of high order Partial Differential Equations (PDEs) by means of NURBS–based Isogeometric Analysis (IGA) in the framework of the Galerkin method, for which global smooth basis functions with degree of continuity higher than C can be used. We derive a priori error estimates for high order elliptic PDEs under h–refinement, by extending existin...