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On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative
On the contact equivalence problem of second order ODEs quadratic second order derivative Differential Geometry
2012/6/19
In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the...
A unified treatment of ODEs under Osgood and Sobolev type conditions
DiPerna–Lions theory Sobolev regularity Osgood condition regular Lagrangian flow transport equation
2011/9/5
Abstract: In this paper we prove the existence, uniqueness and regularity of the DiPerna--Lions flow generated by a vector field which is "almost everywhere Osgood continuous", following Crippa and de...
Equivalence classes of the second order ODEs with the constant Cartan invariant
Invariant Equivalence Problem Ordinary Differential Equation Point transformation Painleve equation Emden equation
2011/7/6
Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent e...
Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs
Finite Element Approximations Numerical Studies Time Approximation Variationally Consis- tent Integral Forms
2013/1/30
The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM ), Galerkin method with weak fo...
Equivalence classes of the second order ODEs with the constant Cartan invariant
Invariant Equivalence Problem Ordinary Differential Equa-tion Point transformation Painleve equation
2011/7/29
Abstract: Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of noneq...
Implementation of 2-point 2-step methods for the solution of first order ODEs
Block methods Ordinary Differential Equation
2010/9/20
In this paper the 2 point 2 step methods (2PG, M2PG, M2PF) for solving system of first order ordinary differential equations are proposed. These methods at each step will approximate the solutions of ...
On a Novel Class of Integrable ODEs Related to the Painlevé Equations
Painlev´ e equation conjugate Painlev´ e equation
2010/12/16
One of the authors has recently introduced the concept of conju-gate Hamiltonian systems: the solution of the equation h = H(p, q, t),where H is a given Hamiltonian containing t explicitly, yields the...
A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
Ordinary differential equations Runge-Kutta methods one-step methods Hamiltonian problems
2010/12/8
In this paper, we provide a simple framework to derive and analyse several classes of effective one-step methods. The framework consists in the discretization of a local Fourier expansion of the conti...
Self-equivalence 3-rd order ODEs by time-¯xed transformations
Lie group Jet bundle Cartan equivalence problem Gardner method of moving frame
2009/1/4
Let y000 = f(x; y; y0; y00) be a 3-rd order ODE. By Cartan equiv-
alence method, we will study the local equivalence problem under the
transformations group of time-¯xed coordinates.
M.S.C. 20...
A Polynomial Time Algorithm to Find Rational General Solutions of First Order Autonomous ODEs
Rational general solution rst order autonomous ODE rational parameterizations Laurent series Pade approximants polynomial time algorithm
2013/9/9
We give a necessary and su±cient condition for an algebraic ODE to have a rational type general solution. For a ˉrst order autonomous ODE F = 0, we give an exact degree bound for its rational solution...
A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no...