Colloquium/Seminar

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Event(s) on March 2006


  • Tuesday, 14th March, 2006

    Title: Recent advances in the numerical analysis of delay differential and integral equations
    Speaker: Prof. Hermann Brunner, Department of Mathematics and Statistics, Memorial University of Newfoundland, and Department of Mathematics, Hong Kong Baptist University
    Time/Place: 11:30  -  12:30
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    Abstract: The numerical analysis of Volterra functional integral and integro-differential equations faces a number of challenges not encountered in delay differential equations. They include the superconvergence analysis of collocation (and discontinuous Galerkin)solutions when the Volterra functional equation contains a singular integral operator and a nonlinear or vanishing delay, and the qualitative analysis of collocation solutions. In this talk I shall review some of the recent -- and ongoing -- work on collocation methods for various classes of Volterra functional equations and point out a number of important open problems.


  • Thursday, 30th March, 2006

    Title: Solvability and Convergence of the Meshless Asymmetric Collocation Method
    Speaker: Dr. Leevan Ling, Department of Applied Mathematics, National Sun Yet-Sen University, Taiwan
    Time/Place: 11:30  -  12:30
    FSC1217
    Abstract: The meshless asymmetric collocation method for solving partial differential equations (PDE) was first proposed in 1990. Although the technique had been very successful in engineering applications, there were no proven results, so far, on the method for solving PDE in strong form. Since the original method cannot be proven to be fail-safe in general, we provide the solvability and convergence of the meshless asymmetric collocation method for a generalized variant. A greedy variation of this technique is provided, allowing a fully adaptive matrix-free and data-dependent meshless selection of the test and trial spaces. Lastly, some numerical results with applications are demonstrated.