相关论文: First order ODEs, Symmetries and Linear Transforma…
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
We identify contact transformations which linearize the given equations in the Riccati and Abel chains of nonlinear scalar and coupled ordinary differential equations to the same order. The identified contact transformations are not of…
We show a general method allowing the solution calculation, in the form of a power series, for a very large class of nonlinear Ordinary Differential Equations (ODEs), namely the real analytic $\sigma\pi$-ODEs (and, more in general, the real…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
Countably infinite systems of linear ODEs arise as forward equations for many continuous-time Markov processes. The standard recipe -- truncate to a finite cap N and exponentiate -- pays cubic cost in N and a time-growing boundary-feedback…
We propose a novel quantum algorithm for solving linear autonomous ordinary differential equations (ODEs) using the Pad\'e approximation. For linear autonomous ODEs, the discretized solution can be represented by a product of matrix…
We have already dealt with the problem of solving First Order Differential Equations (1ODEs) presenting elementary functions before in [1, 2]. In this present paper, we have established solid theoretical basis through a relation between the…
Ordinary differential equations (ODEs) and ordinary difference systems (O$\Delta$Ss) invariant under the actions of the Lie groups $\mathrm{SL}_x(2)$, $\mathrm{SL}_y(2)$ and $\mathrm{SL}_x(2)\times\mathrm{SL}_y(2)$ of projective…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied. The determination of n generalized symmetries of the nth-order…
The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…
The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical…
The order type of a point set in $R^d$ maps each $(d{+}1)$-tuple of points to its orientation (e.g., clockwise or counterclockwise in $R^2$). Two point sets $X$ and $Y$ have the same order type if there exists a mapping $f$ from $X$ to $Y$…
In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…
It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
Identifying integrable coupled nonlinear ordinary differential equations (ODEs) of dissipative type and deducing their general solutions are some of the challenging tasks in nonlinear dynamics. In this paper we undertake these problems and…
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…