Solutions generating technique for Abel-type nonlinear ordinary differential equations
نویسندگان
چکیده
منابع مشابه
Resultant-factorization Technique for Obtaining Solutions to Ordinary Differential Equations
We propose a technique for obtaining solutions to ordinary differential equations. A system of differential equations sometimes has multiple solutions with distinct features. Prime ideal decomposition can be used for extracting the desired solution from these solutions. Solutions to algebraic equations contain many parameters, and in such a case, prime ideal decomposition is less tractable. As ...
متن کاملNonlinear Ordinary Differential Equations
Most physical processes are modeled by differential equations. First order ordinary differential equations, also known as dynamical systems, arise in a wide range of applications, including population dynamics, mechanical systems, planetary motion, ecology, chemical diffusion, etc., etc. See [19, 72,ODES] for additional material and applications. The goal of this chapter is to study and solve i...
متن کاملSolutions Approaching Polynomials at Infinity to Nonlinear Ordinary Differential Equations
This paper concerns the solutions approaching polynomials at ∞ to n-th order (n > 1) nonlinear ordinary differential equations, in which the nonlinear term depends on time t and on x, x′, . . . , x(N), where x is the unknown function and N is an integer with 0 ≤ N ≤ n − 1. For each given integer m with max{1, N} ≤ m ≤ n− 1, conditions are given which guarantee that, for any real polynomial of d...
متن کاملBounds for Solutions of Ordinary Differential Equations
1. An upper bound for the norm of a system of ordinary differential equations can be obtained by comparison with a related first order differential equation, [4; 8]. This first order equation depends on an upper bound for the norm of the right side of the system. Recently, it has been pointed out [l; 6] that this same upper bound also gives a lower bound for the norm of the solution in terms of...
متن کاملNew solutions for ordinary differential equations
This paper introduces a new method for solving ordinary differential equations (ODEs) that enhances existing methods that are primarily based on finding integrating factors and/or point symmetries. The starting point of the new method is to find a non-invertible mapping that maps a given ODE to a related higher-order ODE that has an easily obtained integrating factor. As a consequence, the rela...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2001
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(01)00104-3