Partial differential equations (PDEs) have been successful for solving many problems in image processing and computer vision. However, designing PDEs usually requires high mathematical skills and good insight to the problems. In this paper, we propose a framework for learning a system of PDEs from real data. Compared to the traditional approaches to designing PDEs, our framework requires much l...

In this paper, the homotopyperturbation method (HPM) is employed to obtain approximate analytical solution to the linear and nonlinear systems of partial differential equations (PDEs). HPM yields solutions in convergent series forms with easily computable terms. Generally, the closed form of the exact solution or its expansion is obtained without any noise terms. Test examples demonstrate the e...

improving the quality of medical images at pre and post-surgery operations are necessary for beginning and speeding up the recovery process. partial differential equations (pdes)-based models have become a powerful and well known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. in t...

We develop an optimization-based approach for additive decomposition and reconnection of algebraic problems arising from discretization of partial differential equations (PDEs). Application to a scalar advection-diffusion PDE illustrates the new approach. In particular, we obtain a robust iterative solver for advection-dominated problems using standard multi-level solvers for the Poisson equation.

This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing a barrier option under a certain type of stochastic volatility model including the log-normal SABR model.

We provide an introduction on reduced basis (RB) method for the solution of parametrized partial differential equations (PDEs). We introduce all the main ingredients to describe the methodology and the algorithms used to build the approximation spaces and the error bounds. We consider a model problem describing a steady potential flow around parametrized bodies and we provide some illustrative ...

In this paper, He’s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs). Keywords—Homotopy ...

A new mimetic iterative scheme for solving general biharmonic equations under Robin’s conditions is presented. This approach combines recently developed mimetic techniques for partial differential equations (PDEs) with an efficient iterative scheme based on a global conjugate gradient and a local preconditioned biconjugate gradient methods. The elegant matrix formulation of mimetic methods allo...

We consider a system of semilinear partial differential equations (PDEs) with measurable coefficients and nonlinear Neumann boundary condition. then construct sequence penalized PDEs, which converges to our initial problem. Since the we may be discontinuous, use notion solution in [Formula: see text]-viscosity sense. The method is based on backward stochastic their S-tightness. This work motiva...

The experimental results of improved underwater image enhancement algorithms based on partial differential equations (PDEs) are presented in this report. This second work extends the study of previous work and incorporating several improvements into the revised algorithm. Experiments show the evidence of the improvements when compared to previously proposed approaches and other conventional alg...