Related papers: Whole Line Solutions to Abstract Functional Differ…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…
The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…
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…
We present a fast convolution-based technique for computing an approximate, signed Euclidean distance function $S$ on a set of 2D and 3D grid locations. Instead of solving the non-linear, static Hamilton-Jacobi equation ($\|\nabla S\|=1$),…
The aim of this work is to show an abstract framework to analyze the numerical approximation for a family of linear degenerate parabolic mixed equations by using a finite element method in space and a Backward-Euler scheme in time. We…
A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
In this paper we consider the model semilinear Neumann system $$\left\{ \begin{array}{lll} -\Delta u+a(x)u=\lambda c(x) F_u(u,v)& {\rm in} & \Omega,\\ -\Delta v+b(x)v=\lambda c(x) F_v(u,v)& {\rm in} & \Omega,\\ \frac{\partial u}{\partial…
In this paper, approximate solutions for a class of fractional Lane - Emden type equations based on the series expansion method are presented. Various examples are introduced and discussed. The recurrence relation for the components of the…
We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-\Delta)_{p(\cdot)}^{s}…
We study existence of nontrivial solutions to problem \begin{equation*} \left\lbrace \begin{array}{rcll} -\Delta u &=& \lambda u+f(u)&\text{ in }\Omega,\\ u&=&0&\text{ on }\partial \Omega, \end{array}\right. \end{equation*} where $\Omega…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
We consider a singular fractional differential equation involving generalized Katugampola derivative and obtain the existence and uniqueness of its solution. A scheme for uniformly approximating solution is constructed by using Picard…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
This paper is mainly devoted to describing the entire solutions of nonlinear partial differential equation $$ u_{z_1}u_{z_2}\cdots u_{z_n}=e^g, $$ with the eikonal equation as a prototype, where $g$ is a polynomial in $\mathbb{C}^n$.…
We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.
In this work the implicit function theorem is used for searching local symbolic resolution of differential equations. General results of existence for first order equations are proven and some examples, one relative to cavitation in a…