Related papers: Numerical solution of a certain type of integral e…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
At present, only some special differential equations have explicit analytical solutions. In general, no one thinks that it is possible to analytically find the exact solution of nonlinear equations. In this article based on the idea that…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
It is proved that nonlinear integral equations of certain class have global solution and estimates of the solution are given as $t\to \infty$.
We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
This work develops a class of probabilistic algorithms for the numerical solution of nonlinear, time-dependent partial differential equations (PDEs). Current state-of-the-art PDE solvers treat the space- and time-dimensions separately,…
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In…
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to viscosity solutions. We begin by describing a fundamental…