Related papers: Python Classes for Numerical Solution of PDE's
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
We analyze the polynomial solutions of the linear differential equation $p_2(x)y''+p_1(x)y'+p_0(x)y=0$ where $p_j(x)$ is a $j^{\rm th}$-degree polynomial. We discuss all the possible polynomial solutions and their dependence on the…
We present Elvet, a Python package for solving differential equations and variational problems using machine learning methods. Elvet can deal with any system of coupled ordinary or partial differential equations with arbitrary initial and…
SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85\%)…
In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the…
We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this…
We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide…
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
In this paper, we present numerical procedures to compute solutions of partial differential equations posed on fractals. In particular, we consider the strong form of the equation using standard graph Laplacian matrices and also weak forms…
Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…