1,841 research outputs found
A fractional B-spline collocation method for the numerical solution of fractional predator-prey models
We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost
Cumulative reports and publications through December 31, 1988
This document contains a complete list of ICASE Reports. Since ICASE Reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
An unconditionally stable space-time isogeometric method for the acoustic wave equation
We study space--time isogeometric discretizations of the linear acoustic wave
equation that use B-splines of arbitrary degree , both in space and time. We
propose a space--time variational formulation that is obtained by adding a
non-consistent penalty term of order to the bilinear form coming from
integration by parts. This formulation, when discretized with tensor-product
spline spaces with maximal regularity in time, is unconditionally stable: the
mesh size in time is not constrained by the mesh size in space. We give
extensive numerical evidence for the good stability, approximation, dissipation
and dispersion properties of the stabilized isogeometric formulation, comparing
against stabilized finite element schemes, for a range of wave propagation
problems with constant and variable wave speed
Cumulative reports and publications through December 31, 1990
This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available
Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales
In this paper, we consider numerical homogenization of acoustic wave
equations with heterogeneous coefficients, namely, when the bulk modulus and
the density of the medium are only bounded. We show that under a Cordes type
condition the second order derivatives of the solution with respect to harmonic
coordinates are (instead with respect to Euclidean coordinates)
and the solution itself is in (instead of
with respect to Euclidean coordinates). Then, we
propose an implicit time stepping method to solve the resulted linear system on
coarse spatial scales, and present error estimates of the method. It follows
that by pre-computing the associated harmonic coordinates, it is possible to
numerically homogenize the wave equation without assumptions of scale
separation or ergodicity.Comment: 27 pages, 4 figures, Submitte
Cumulative reports and publications
A complete list of Institute for Computer Applications in Science and Engineering (ICASE) reports are listed. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available. The major categories of the current ICASE research program are: applied and numerical mathematics, including numerical analysis and algorithm development; theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and computer science
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