1,841 research outputs found

    A fractional B-spline collocation method for the numerical solution of fractional predator-prey models

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    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

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    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

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    We study space--time isogeometric discretizations of the linear acoustic wave equation that use B-splines of arbitrary degree pp, both in space and time. We propose a space--time variational formulation that is obtained by adding a non-consistent penalty term of order 2p+22p+2 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

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    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

    STOKES APPROXIMATION SOLUTIONS FOR STEEP STANDING WAVES

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    Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales

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    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 L2L^2 (instead H−1H^{-1} with respect to Euclidean coordinates) and the solution itself is in L∞(0,T,H2(Ω))L^{\infty}(0,T,H^2(\Omega)) (instead of L∞(0,T,H1(Ω))L^{\infty}(0,T,H^1(\Omega)) 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

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    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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