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M. T. Mustafa

  1. Polynomial Solutions of Differential Equations.

    Втр, 02/23/2010 - 16:01 — SomNambul
    Authors: H. Azad, M. T. Mustafa
    Subjects: Classical Analysis and ODEs
    Abstract

    We show that any differential operator of the form $L(y)=\sum_{k=0}^{k=N}
    a_{k}(x) y^{(k)}$, where $a_k$ is a real polynomial of degree $\leq k$, has all
    real eigenvalues in the space of polynomials of degree at most n, for all n.
    The eigenvalues are given by the coefficient of $x^n$ in $L(x^{n})$.

  2. Sturm-Liouville Theory and Orthogonal Functions.

    Пт, 10/02/2009 - 09:41 — SomNambul
    Authors: H. Azad, M. T. Mustafa
    Subjects: Classical Analysis and ODEs
    Abstract

    We revisit basics of classical Sturm-Liouville theory and, as an application,
    recover Bochner's classification of second order ODEs with polynomial
    coefficients and polynomial solutions by a new argument. We also outline how a
    wider class of equations with polynomial solutions can be obtained by allowing
    the weight to become infinite at isolated points:the Jacobi equation, in
    general, is of this type.

  3. Sturm-Liouville Theory and Orthogonal Functions.

    Пт, 10/02/2009 - 09:41 — SomNambul
    Authors: H. Azad, M. T. Mustafa
    Subjects: Classical Analysis and ODEs
    Abstract

    We revisit basics of classical Sturm-Liouville theory and, as an application,
    recover Bochner's classification of second order ODEs with polynomial
    coefficients and polynomial solutions by a new argument. We also outline how a
    wider class of equations with polynomial solutions can be obtained by allowing
    the weight to become infinite at isolated points:the Jacobi equation, in
    general, is of this type.

  4. Analytic solutions of initial-boundary-value problems of transient conduction using symmetries.

    Пнд, 09/07/2009 - 10:33 — SomNambul
    Authors: H. Azad, M. T. Mustafa, A. F. M. Arif
    Subjects: Analysis of PDEs
    Abstract

    Lie symmetry method is applied to find analytic solutions of
    initial-boundary-value problems of transient conduction in semi-infinite solid
    with constant surface temperature or constant heat flux condition. The
    solutions are obtained in a manner highlighting the systematic procedure of
    extending the symmetry method for a PDE to investigate BVPs of the PDE. A
    comparative analysis of numerical and closed form solutions is carried out for
    a physical problem of heat conduction in a semi-infinite solid bar made of AISI
    304 stainless steel.

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