a meshless method namely, discrete least square method (dlsm), is presented in the paper for the solution of free surface seepage problem. in this method computational domain is discredited by some nodes and then the set of simultaneous equations are built using moving least square (mls) shape functions and least square technique. the proposed method does not need any background mesh therefore ...

New General Ray (GR) method for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. GRmethod consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the Laplace, Poisson and Helmgoltz equations. GRmethod pr...

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the s...

New fast algorithms for solution of the Dirichlet boundary value problem for the class of elliptic Partial Differential Equations (PDE) is proposed. Algorithms are based on new version of General Ray (GR) method which consists in application of the Radon transform directly to the PDE and in reduction PDE to assemblage of Ordinary Differential Equations (ODE). The class of the PDE includes the L...

We consider a task of tracing out target figures hidden in teeming figure pictures come to known as Wimmelbild(er). Wimmelbild is a popular genre of visual puzzles; a timeless classic for children, artists and cognitive scientists. Particularly suited to the considered task, we propose a diffuse representation which serves as a heuristic approximation mimicking curvature coding distance images....

The Finite Element Method (FEM) introduced by engineers in late 50's and 60's is a numerical technique for solving problems which are described by Ordinary Differential Equations (ODE) /Partial Differential Equations (PDE) with appropriate boundary/initial conditions or to solve problems that can be formulated as a functional minimization. FEM provides greater flexibility to model complex geome...

By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thi...

We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian the transitions are driven by Poisson random clocks. a case where there two different scales: microscopic one with fast dynamic macroscopic slow dynamic. At level, species abundant for large population limit partial differential equation (PDE) obtained. On contrary at not ...