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Showing 1 to 20 of 36 for “"Initial Value Problems"”.
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Explicit approximation methods for initial-value problems
Explicit difference approximations of parabolic initial boundary value problems are usually stable only if a difference grid with a limited time-step is used. By considering the one-dimensional diffusion equation as an example, it is shown in the following work that simple smoothing formulas can be …
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Bounds for linear and nonlinear initial value problems
Digitized by Kansas Correctional Industries
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Bounds for linear and nonlinear initial value problems
Digitized by Kansas Correctional Industries
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Initial Value Problems for Creeping Flow of Maxwell Fluids
… We study the well-posedness of the resulting PDE initial-boundary value problem. This well-posedness depends on the unique solvability of an elliptic boundary value problem. We first present results for the 3D case, locally and globally in time, with sufficiently small initial data, and for a …
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Boundary data smoothness for solutions of nonlocal boundary value problems for nth order differential equations.
… involves application of Peano's Theorem for initial value problems.
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Dynamics and Asymptotic Behavior of the Solutions of a Nonlinear Differential Equation
Initial value problems of the form dx/dt= t xP, x(a) = β are examined, first when p = 2. Applying Euler's method, a numerical approximation technique, when p = 2 for certain initial conditions produces a numerical solution which resembles a bifurcation diagram very similar to that produced by the …
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Συνεχείς επεκτάσεις μεθόδων Runge-Kutta για προβλήματα αρχικών τιμών
… of Runge-Kutta algorithms when solving initial value problems. We consider two ways (I) scaling (II) interpolation. The same extension was done for Runge-Kutta-Nystrom methods for initial value problem of second class.
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INTERPOLATION OF RIGID-BODY MOTION AND GALERKIN METHODS FOR FLEXIBLE MULTIBODY DYNAMICS
Traditionally, flexible multibody dynamics problems are formulated as initial value problems: initial states of the system are given and solving for the equations of motion yields the dynamic response. Many practical problems, however, are boundary rather than initial value problems; two-point and …
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Controllability, Observability and Realizability
… a new method for computing the approximate values of matrix exponentials, and use this to estimate solutions to initial value problems.
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Adaptive Geometric Numerical Integration of Mechanical Systems
… structure preserving numerical integration of initial value problems, i.e., so called geometric numerical integrators. In particular, we are interested in how time-step adaptivity can be achieved in conjunction with structure preserving properties without destroying the good long time …
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Opial's Inequality on Time Scales and an Application
… that concerns upper bound estimates of Dynamic Initial Value Problems and illustrate the usage of the developed Dynamic Opial Inequality.</p>
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Opial's Inequality on Time Scales and an Application
… that concerns upper bound estimates of Dynamic Initial Value Problems and illustrate the usage of the developed Dynamic Opial Inequality.
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Time Stepping Methods for Multiphysics Problems
Mathematical modeling of physical processes often leads to systems of differential and algebraic equations involving quantities of interest. A computer model created based on these equations can be numerically integrated to predict future states of the system and its evolution in time. This thesis …
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Time Integration Methods for Large-scale Scientific Simulations
The solution of initial value problems is a fundamental component of many scientific simulations of physical phenomena. In many cases these initial value problems arise from a method of lines approach to solving partial differential equations, resulting in very large systems of equations that …
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Periodic existence theorems in optimal control
… a general existence theorem for such control problems. This existence theorem requires finding bounds on a Hamiltonian function. In his work Rockafellar specialized his results to certain initial value problems. The central new theorems in this paper specialize Rockafellar's general theorem to …
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On Differential Equations With Indefinite Principal Parts
… comprise chapters 2-4 herein. They deal with problems arising from a study of various differential equations with indefinite principal parts whether they be classified as ordinary, abstract, or fractional. In the first paper (Chapter 2) we show that Sturm’s separation theorem always fails for …
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Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs
In the initial value problems (IVPs) describing evolutions, the dependent variables naturally exhibit simultaneous dependence on spatial coordinates and time. Thus, space-time coupled methods of approximation are rather natural for obtaining numerical solutions of the mathematical models (IVPs) …
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Theoretical methods for the study of quantum dynamics
… principle of stationary action applicable to initial-value problems. This has resulted in the first reported synthetic computation of non-stationary quantum trajectories for a fully anharmonic oscillator. Success in one dimension has laid the groundwork for future extension to a rigorous …
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