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Displaying 321 –
340 of
511
We consider the numerical solution of diffusion problems in (0,T) x Ω for and for T > 0 in
dimension dd ≥ 1. We use a wavelet based sparse grid
space discretization with mesh-width h and order pd ≥ 1, and
hp discontinuous Galerkin time-discretization of order on a geometric sequence of many time
steps. The linear systems in each time step are solved iteratively
by GMRES iterations with a wavelet preconditioner.
We prove that this algorithm gives an L2(Ω)-error of
O(N-p) for u(x,T)...
A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate...
Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level (i.e., mean values of old and new time step) to (i.e., only from new time step). Stable solution was obtained only for schemes...
We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...
We deal with numerical analysis and simulations of the Davey-Stewartson equations
which model, for example, the evolution of water surface waves.
This time dependent PDE system is particularly interesting as a generalization
of the 1-d integrable NLS to 2 space dimensions.
We use a time splitting spectral method where
we give a convergence analysis for the semi-discrete version of the scheme.
Numerical results are presented for various blow-up phenomena of
the equation, including blowup of defocusing,...
We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech. 42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...
We propose a Diphasic Low Mach Number (DLMN) system for the modelling of diphasic flows without phase change at low Mach number, system which is an extension of the system proposed by Majda in [Center of Pure and Applied Mathematics, Berkeley, report No. 112] and [Combust. Sci. Tech.42 (1985) 185–205] for low Mach number combustion problems. This system is written for a priori any equations of state. Under minimal thermodynamic hypothesis which are satisfied by a large class of generalized van...
We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in order to be applicable to a logarithmic free energy. Finally numerical experiments with...
We consider a model for phase separation of
a multi-component alloy with non-smooth free energy
and a degenerate mobility matrix. In addition to showing
well-posedness and stability bounds for
our approximation, we prove convergence in one space dimension.
Furthermore an iterative scheme for solving the
resulting nonlinear discrete system is analysed.
We discuss also how our approximation has to be modified in order
to be applicable to a logarithmic free energy.
Finally numerical experiments...
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary value problem...
Currently displaying 321 –
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