Related papers: The method of solving a scalar initial value probl…
In this study, we employ Euler's method and Richardson's extrapolation to solve a triple integral, which is then transformed into a third-order initial value problem. Our objective is to resolve the computational challenges associated with…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…
This article analyzes and develops a method to solve fractional ordinary differential equations using the Monte Carlo Method. A numerical simulation is performed for some differential equations, comparing the results with what exists in the…
The double-exponential Sinc-collocation method is known as a super-accurate method for solving initial value problems of ordinary differential equations, for which the error decreases almost exponentially as a function of the number of…
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
The paper deals with the following system of nonlinear difference equations \begin{equation*} x_{n+1}=ax_{n}^{2}y_{n}+bx_{n}y_{n}^{2},\ y_{n+1}=cx_{n}^{2}y_{n}+dx_{n}y_{n}^{2},\ n\in \mathbb{N}_{0}, \end{equation*} where the initial values…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
The main goal of this paper is to construct the so-called Birkhoff-type solutions for linear ordinary differential equations with a spectral parameter. Such solutions play an important role in direct and inverse problems of spectral theory.…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
In this work, we present some new integration formulas for any order of accuracy as an application of the B-spline relations obtained in [1]. The resulting rules are defined as a perturbation of the trapezoidal integration method. We prove…
In the recent breakthrough work \cite{xu2023lack}, a rigorous numerical analysis was conducted on the numerical solution of a scalar ODE containing a cubic polynomial derived from the Allen-Cahn equation. It was found that only the implicit…
We study initial value problem for a system consisting of an integer order and distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. Explicit form of…
A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. Such classes of problems occur frequently in Quantum Mechanics and Optics. This approach…