In this paper, we study different numerical methods for solving fuzzy equations, dual differential equations (FDEs) and partial (PDEs). study, conditions that guarantee the existence of roots these are discussed. Also, paper provides some discussion about rates convergence each methods. Finally, examples given to illustrate efficiency

In this paper, we will present a comparison between the Adomian Decomposition Method (ADM) and Taylor Matrix Method by solving some well-known partial differential equations (PDEs). In order to illustrate the analysis we examined the Telegraph equation, which is considered one of the most significant partial differential equations, describe wave propagation of electric signals in a cable transm...

Multigrid (MG) methods are used to approximate solutions to elliptic partial differential equations (PDEs) by iteratively improving the solution through a sequence of coarser discretizations or grids. The methodology has been developed and extended since the 1970’s to also target more general PDEs and systems of algebraic equations. A typical approach consists of a series of refinements or grid...

A number of image denoising models based on higher order parabolic partial differential equations (PDEs) have been proposed in an effort to overcome some of the problems attendant to second order methods such as the famous Perona-Malik model. However, there is little analysis of these equations to be found in the literature. In this paper, methods of maximal regularity are used to prove the exi...

We introduce a general, analytical framework to express and approximate partial differential equations (PDEs) numerically on graphs networks of surfaces – generalized by the term hypergraphs. To this end, we consider PDEs hypergraphs as singular limits in thin domains (such fault planes, pipes, etc.), observe that (mixed) hybrid formulations offer useful tools formulate such PDEs. Thus, our num...

Many physical applications require the solution of a system of coupled partial differential equations (PDEs). In most cases the analytic PDE solution does not exist for this system and we need to solve the problem numerically using the finite element method in COMSOL. This paper presents information on techniques needed in COMSOL 4 to enable computational studies of coupled systems of PDEs for ...

Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is impleme...

To restore the underexposure image, an illumination compensation inpainting model which employs the joint-diffused partial differential equations (PDEs) is proposed. Firstly, the novel model compensates the illumination effect in multi-scaled underexposure images respectively. Secondly, the information in the fused compensated image is restored by PDEs which diffuse the geometric property and g...

Multi-symplectic methods have recently been considered as a generalization of symplectic ODE methods to the case of Hamiltonian PDEs. The symplectic of Hamiltonian systems is well known, but for Partial Differential Equation (PDEs) this is a global property. In addition, many PDEs can be written as Multisymplectic systems, in which each independent variable has a distinct symplectic structure. ...

Schwarz waveform relaxation methods have been studied for a wide range of scalar linear partial differential equations (PDEs) of parabolic and hyperbolic type. They are based on a space-time decomposition of the computational domain and the subdomain iteration uses an overlapping decomposition in space. There are only few convergence studies for non-linear PDEs. We analyze in this paper the con...