Relations between generalized solutions of ordinary differential equations
نویسندگان
چکیده
منابع مشابه
Bounds 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 کاملWavelet Galerkin Solutions of Ordinary Differential Equations
Abstract. Advantage of wavelet Galerkin method over finite difference or element method has led to tremendous applications in science and engineering. In recent years there has been increasing attempt to find solutions of differential equations using wavelet techniques. In this paper, we elaborate the wavelet techniques and apply Galerkin procedure to analyse one dimensional harmonic wave equat...
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 کاملGeneralized Derivatives for Solutions of Parametric Ordinary Differential Equations with Non-differentiable Right-Hand Sides
Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic systems embedded is a challenging task. In this article, for any locally Lipschitz continuous mapping between finitedimensional Euclidean spaces, Nesterov’s lexicographic derivatives are shown to b...
متن کاملExistence of generalized solutions for ordinary differential equations in Banach spaces ∗
1. Introduction We will be considering the existence of solutions of ordinary differential equations in Banach spaces, taking these to have the nominal form (1.1) ˙ x = Ax + f (x), x(0) = ˆ ξ 0 on some interval [0, T ]. Here x(·) takes values in the Banach space X and A is the infinitesimal generator of a C 0 semigroup S(·) of linear operators on X .f : X → X. We are indebted to [8] for an exce...
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: Časopis pro pěstování matematiky
سال: 1976
ISSN: 0528-2195
DOI: 10.21136/cpm.1976.117903