We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the gradient of the solution playing the role of the policy function, and the loss function given by the error between the prescribed terminal condition and the solut...

We develop a level set method for the computation of multivalued solutions to quasi-linear hyperbolic partial differential equations and Hamilton-Jacobi equations in any number of space dimensions. We use the classic idea of Courant and Hilbert to define the solution of the quasi-linear hyperbolic PDEs or the gradient of the solution to the Hamilton-Jacobi equations as zero level sets of level ...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...

We present here, a Haar wavelet method for a class of third order partial dierentialequations (PDEs) arising in impulsive motion of a flat plate. We also, present Adomaindecomposition method to find the analytic solution of such equations. Efficiency andaccuracy have been illustrated by solving numerical examples.

The collective movements of unicellular organisms such as bacteria or amoeboid (crawling) cells are often modeled by partial differential equations (PDEs) that describe the time evolution of cell density. In particular, chemotaxis equations have been used to model the movement towards various kinds of extracellular cues. Well-developed analytical and numerical methods for analyzing the time-dep...

There is an increasing demand to develop image processing tools for the filtering and analysis of matrix-valued data, so-called matrix fields. In the case of scalar-valued images parabolic partial differential equations (PDEs) are widely used to perform filtering and denoising processes. Especially interesting from a theoretical as well as from a practical point of view are PDEs with singular d...

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

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

In this paper, we deal with the problem of computing the distance to a surface (a curve in 2D) and consider several distance function approximation methods which are based on solving partial differential equations (PDEs) and finding solutions to variational problems. In particular, we deal with distance function estimation methods related to the Poisson-like equations and generalized double-lay...

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating ...