Related papers: Numerical Solution of Initial Value Problems
The explicit solution of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODE s with second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary (time-independent)…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…
A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We study local, analytic solutions for a class of initial value problems for singular ODEs. We prove existence and uniqueness of such solutions under a certain non-resonance condition. Our proof translates the singular initial value problem…
We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees…
The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial and boundary…
An initial-value problem for an ordinary differential equation of the first order, is considered. It is supposed that the right-hand side of the equation is a continuous function defined on a set consisting of an open set and a part of its…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical…
Many Engineering Problems could be mathematically described by Final Value Problem, which is the inverse problem of Initial Value Problem. Accordingly, the paper studies the final value problem in the field of ODE problems and analyses the…
Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In \cite{PS2}, we have presented the first algorithmic way to deal with SOODEs, introducing the basis for the…
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…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization.…
Given a linear ordinary differential equation (ODE) on $\RE$ and a set of interface conditions at a finite set of points $I \subset \RE$, we consider the problem of determining another differential equation whose {\it global} solutions…
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…