Related papers: Linearization of ODEs: algorithmic approach
The standard methodology handling nonlinear PDE's involves the two steps: numerical discretization to get a set of nonlinear algebraic equations, and then the application of the Newton iterative linearization or its variants to solve the…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
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…
Classification of $n-$th $(n\geq2)$ order linear ODEs is considered. The equation reduced to \textit{Laguerre-Forsyth} form by a point transformation then, the other calculations would have done on this form. This method is due to…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
The Integration Theory of Linear Ordinary Differential Equation.
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…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…
Linearization is the procedure of rewriting a process term into a linear form, which consist only of basic operators of the process language. This procedure is interesting both from a theoretical and a practical point of view. In…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from…
We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…
Quantification, i.e., the task of training predictors of the class prevalence values in sets of unlabeled data items, has received increased attention in recent years. However, most quantification research has concentrated on developing…
The linearization problem for nonlinear second-order ODEs to the Laguerre form by means of generalized Sundman transformations (S-transformations) is considered, which has been investigated by Duarte et al. earlier. A characterization of…
We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain…