Related papers: Numerical Computation of Takens-Bogdanov Points fo…
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…
In this work we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large--scale systems of quadratic autonomous Ordinary Differential Equations (ODEs) modeling, e.g., the…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
The delay Lyapunov equation is an important matrix boundary-value problem which arises as an analogue of the Lyapunov equation in the study of time-delay systems $\dot{x}(t) = A_0x(t)+A_1x(t-\tau)+B_0u(t)$. We propose a new algorithm for…
In this paper, we prove the existence and uniqueness of the solution for neutral stochastic differential delay equations with locally monotone coefficients by using numerical approximation. An example is provided to illustrate our theory.
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method.…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
We consider the problem of finding the shortest possible period for an exactly periodic solution to some given autonomous ordinary differential equation. We show that, given a pair of Lyapunov-like observable functions defined over the…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations…
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…
Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…