Related papers: An analytical approximation scheme to two point bo…
In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability…
Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often…
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…
We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…
This paper is a sequel of our previous work in which we introduced the MapDE algorithm to determine the existence of analytic invertible mappings of an input (source) differential polynomial system (DPS) to a specific target DPS, and…
We present a method to design parallel algorithms for constrained combinatorial optimization problems. Our method solves and generalizes many classical combinatorial optimization problems including the stable marriage problem, the shortest…
A numerical algorithm to solve the spectral problem for arbitrary self-adjoint extensions of 1D regular Schroedinger operators is presented. It is shown that the set of all self-adjoint extensions of 1D regular Schroedinger operators is in…
This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection…
This paper considers the numerical solution of Timoshenko beam network models, comprised of Timoshenko beam equations on each edge of the network, which are coupled at the nodes of the network using rigid joint conditions. Through…
A pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations (ODEs) is proposed in this study. The method is particularly suitable for the analysis of systems that feature distinct…
For the ordinary differential equation (ODE) $\dot{x}(t) = f(t,x)$, $x(0) = x_0$, $t\geq 0$, $x\in R^d$, assume $f$ to be at least continuous in $t$ and locally Lipshitz in $x$, and if necessary, several times continuously differentiable in…
Estimating the parameters of ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODEs are typically approximated with deterministic algorithms, new research on probabilistic solvers…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to…
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…
The main goal of this thesis is to show the crucial role that plays the symbol in analysing the spectrum the sequence of matrices resulting from PDE approximation and in designing a fast method to solve the associated linear problem. In the…
The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…