Results 241 to 250 of about 789,164 (294)

Optimal approximation of the initial value problem

open access: yesComputers and Mathematics With Applications, 1998
We construct an optimal approximation procedure for the resolution of the initial value problem by using the optimal ...
O Arino
exaly   +2 more sources

An initial–boundary value problem for the Maxwell equations

open access: yesJournal of Differential Equations, 2010
In this paper, by using methods from complex analysis and quaternionic analysis, we investigate an initial–boundary value problem for the Maxwell equations and obtain the general solutions and solvable conditions of the problem respectively in different ...
Li, Manli   +5 more
exaly   +2 more sources

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.
Bell, C. A., Appl, F. C.
openaire   +1 more source

On the numerical study of nonlinear initial-boundary value problems or initial-value problems

Applied Mathematics and Computation, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zaki F. A. El-Reheem, A. H. Nasser
openaire   +1 more source

The Periodic Initial Value Problem and Initial Value Problem for the Modified Boussinesq Approximation

Journal of Partial Differential Equations, 2002
Summary: The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds frequent use in geological practice. In this paper, we consider the periodic initial value problem and initial value problem for this modified Boussinesq approximation with the viscous part of the stress tensor \(\tau^v=\tau ({\mathbf e})-2 \mu_1 ...
Guo, Boling, Shang, Yadong
openaire   +2 more sources

Initial-Value Problems for ODE

2012
The ability to reliably solve initial-value problems for ordinary differential equations is essential in order to understand the evolution of dynamical systems. In this chapter we deal with methods of advancing the given initial state of a system to later times, explaining clearly the role of stiffness, local discretization and round-off errors, and ...
Simon Širca, Martin Horvat
openaire   +1 more source

Rapidly Forced Initial Value Problems

SIAM Journal on Applied Mathematics, 1993
The Cauchy problem for the evolution equation of the type \(u_ t + u_{xx} = f(x,t/ \varepsilon)\), \(t>0\), \(x \in \mathbb{R}^ 1\), with smooth initial function is considered. The function \(f(x, \tau)\) is periodic in \(\tau\). An asymptotic expansion of the solution as \(\varepsilon\to 0\) is constructed in the form of the \(\varepsilon\)-power ...
openaire   +2 more sources

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