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About 10,000 papers for “Initial value problem”

Fuzzy initial value problem

Saïd Melliani, Lalla Saâdia Chadli, M. Atraoui et al. · SHILAP Revista de lepidopterología · 2015

In this paper, we present the fuzzy solution concept of the initial value problem. After introducing a metric between two fuzzy vectors, we prove that the system of fuzzy equations has unique solution under some condition.

Cited by 0Open access

Fuzzy fractional initial value problem

P. Prakash, Juan J. Nieto, S. Senthilvelavan et al. · Journal of Intelligent & Fuzzy Systems · 2015

Abstract We consider initial value problems for differential equations of fractional order with uncertainty and present the theory and some numerical methods to solve such type of problems under generalized differentiability conditions. The main tool is Banach fixed point theorem. Also we study the numerical approximation of the solutions of a fuzzy fractional initial value problem by using product trapezoidal and product rectangle formulas; the convergence of the numerical scheme is analyzed rigorously. Finally some numerical examples are provided to illustrate the applicability and usefulness of the obtained results.

Cited by 25

The Initial-Value Problem for . . .

W. O. Criminale, T. L. Jackson, D. G. Lasseigne · 2012

Plane viscous channel flows are perturbed and the ensuing initial-value problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this work offers a means whereby completely arbitrary initial input can be speci ed without having to resort to eigenfunction expansions. The full temporal behavior, including both early time transients and the long time asymptotics, can be determined for any initial disturbance. Effects of three-dimensionality can be assessed. The bases for the analysis are: (a) linearization of the governing equations; (b) Fourier decomposition in the spanwise and streamwise directions of the ow and; (c) direct numerical integration of the resulting partial differential equations. All of the stability data that are known for such flows can be reproduced. Also, the optimal initial conditions can be determined in a straight forward manner and such optimal conditions clearly reflect transient growth data that is easily determined by a rational choice of a basis for the initial conditions. Although there can be signi cant transient growth for subcritical values of the Reynolds number using this approach, it does not appear possible that arbitrary initial conditions will lead to the exceptionally large transient amplitudes that have been determined by optimization of normal modes. The approach is general and can be applied to other classes of problems where only a finite discrete spectrum exists, such as the boundary layer for example.

Cited by 0

The characteristic initial value problem

John M. Stewart · Cambridge University Press eBooks · 1991

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Cited by 7

The Periodic Initial Value Problem and Initial Value Problem for the Non-Newtonian Boussinesq Approximation

Lin Wei, Boling Guo, Yadong Shang · Applicable Analysis · 2003

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In this article, we consider the periodic initial value problem and initial value problem for the non-Newtonian Boussinesq equations describing the behavior of flows of an incompressable viscous fluid in processes where the thermal effects play an essential role. The existence of weak solution is proved for p ≥2, its uniqueness and regularity for p>(1+2n/(n+2)).

Cited by 3