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Doctoral Degrees (Mathematics and Computer Science Education)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7140

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Browsing Doctoral Degrees (Mathematics and Computer Science Education) by Author "Banasiak, Jacek."

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    Amplitude-shape method for the numerical solution of ordinary differential equations.
    (1997) Parumasur, Nabendra.; Banasiak, Jacek.; Mika, Janusz R.
    In this work, we present an amplitude-shape method for solving evolution problems described by partial differential equations. The method is capable of recognizing the special structure of many evolution problems. In particular, the stiff system of ordinary differential equations resulting from the semi-discretization of partial differential equations is considered. The method involves transforming the system so that only a few equations are stiff and the majority of the equations remain non-stiff. The system is treated with a mixed explicit-implicit scheme with a built-in error control mechanism. This approach proved to be very effective for the solution of stiff systems of equations describing spatially dependent chemical kinetics.
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    Coagulation-fragmentation dynamics in size and position structured population models.
    (2008) Noutchie, Suares Cloves Oukouomi.; Banasiak, Jacek.
    One of the most interesting features of fragmentation models is a possibility to breach
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    A new approach to ill-posed evolution equations : C-regularized and B- bounded semigroups.
    (2001) Singh, Virath Sewnath.; Banasiak, Jacek.
    The theory of semigroups of linear operators forms an integral part of Functional Analysis with substantial applications to many fields of the natural sciences. In this study we are concerned with the application to equations of mathematical physics. The theory of semigroups of bounded linear operators is closely related to the solvability of evolution equations in Banach spaces that model time dependent processes in nature. Well-posed evolution problems give rise to a semigroup of bounded linear operators. However, in many important and interesting cases the problem is ill-posed making it inaccessible to the classical semigroup theory. One way of dealing with this problem is to generalize the theory of semigroups. In this thesis we give an outline of the theory of two such generalizations, namely, C-regularized semigroups and B-bounded semigroups, with the inter-relations between them and show a number of applications to ill-posed problems.