Results 321 to 330 of about 3,263,025 (375)

Initial Value Problems

2017
This chapter is devoted to initial values problems for ordinary differential equations. It discusses theory for existence, uniqueness and continuous dependence on the data of the problem. Special techniques for linear ordinary differential equations with constant coefficients are discussed in terms of matrix exponentials and their approximations. Next,
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Bounds for Initial Value Problems

Journal of Applied Mechanics, 1973
A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type: x(¨t)+f(t,x,x)˙=0,x(0)=X0,x(˙0)=V0, where f is continuous with continuous first derivatives, Lipschitzian, and ∂f/∂x ≥ 0.
F. C. Appl, C. A. Bell
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Initial Value Problems in Viscoelasticity

Applied Mechanics Reviews, 1988
We review some recent mathematical results concerning integrodiff erential equations that model the motion of one-dimensional nonlinear viscoelastic materials. In particular, we discuss global (in time) existence and long-time behavior of classical solutions, as well as the formation of singularities in finite time from smooth initial data.
Michael Renardy, John A. Nohel, William J. Hrusa   +2 more
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Initial value problem for hybrid $$\psi $$-Hilfer fractional implicit differential equations

Journal of Fixed Point Theory and Applications, 2021
A. Salim, M. Benchohra, J. Graef, J. Lazreg   +3 more
semanticscholar   +1 more source

Transformation of a Boundary Value Problem to an Initial Value Problem

1985
The method for transforming nonlinear boundary value problems to initial value problems was first introduced by Toepfer1 in 1912 in his attempt to solve Blasius’ equation in boundary layer theory by a series expansion method. About half a century later Klamkin2, based on the same reasoning, extended the method to a wider class of problems.
R. Seshadri, T. Y. Na
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Condition of Initial Value Problems

2002
In this chapter we consider again initial value problems, which, if not otherwise stated, have the explicit form $$x'\, = \,f\left( {t,\,x} \right),\,\,\,\,\,\,\,x\left( {t_0 } \right)\, = \,x_0.$$
Folkmar Bornemann, Peter Deuflhard
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Characteristics and Initial-Value Problems

1983
Roughly speaking, characteristics are curves which carry information. They are particularly relevant in the study of “initial-value” problems ; that is, in solving partial differential equations, in which the solution surface is required to assume prescribed values “initially.” Such a problem presupposes the existence of a distinguished coordinate, ξ ...
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On the initial-value problem for a wavemaker

Journal of Fluid Mechanics, 1991
The linearized initial-value problem for the generation of straight-crested waves in a deep, inviscid liquid in response to the prescribed motion of a piston wavemaker of finite depth is solved through integral transforms. The indicial admittance (the surface-wave response to a step-function velocity of the wavemaker) is cast in similarity form and ...
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A new approach to non-homogeneous fuzzy initial value problem

, 2012
In this paper, we consider a high-order linear differential equation with fuzzy forcing function and with fuzzy initial values. We assume the forcing function be in a special form, which we call triangular fuzzy function.
N. Gasilov, I. Hashimoglu, S. E. Amrahov, A. G. Fatullayev   +3 more
semanticscholar   +1 more source

Applications of the Initial Value Problem

1987
In this chapter, we shall consider specific kinetic models related to the transport of neutrons and electrons, and to cellular growth. The first two sections will be devoted to neutron transport, with special attention to spectral properties of the full transport operator and implications to hydrodynamics.
Vladimir Protopopescu, William Greenberg, Cornelis van der Mee   +2 more
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