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  • Open Access

    ARTICLE

    Space-Time Adaptive Fup Multi-Resolution Approach for Boundary-Initial Value Problems

    Hrvoje Gotovac1, Vedrana Kozulić2, Blaž Gotovac1

    CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 173-198, 2010, DOI:10.3970/cmc.2010.015.173

    Abstract The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the threshold as a direct measure… More >

  • Open Access

    ARTICLE

    A Fictitious Time Integration Method for Solving Delay Ordinary Differential Equations

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.10, No.1, pp. 97-116, 2009, DOI:10.3970/cmc.2009.010.097

    Abstract A new numerical method is proposed for solving the delay ordinary differential equations (DODEs) under multiple time-varying delays or state-dependent delays. The finite difference scheme is used to approximate the ODEs, which together with the initial conditions constitute a system of nonlinear algebraic equations (NAEs). Then, a Fictitious Time Integration Method (FTIM) is used to solve these NAEs. Numerical examples confirm that the present approach is highly accurate and efficient with a fast convergence. More >

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