Faculty Publications

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Author: search.filters.author.Godavarma, G.Subject: search.filters.subject.Quasilinearization

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    Iterative methods for a fractional-order Volterra population model
    (Rocky Mountain Mathematics Consortium PO Box 871804 Tempe AZ 85287-1804, 2019) Roy, R.; Vijesh, V.A.; Godavarma, G.
    We prove an existence and uniqueness theorem for a fractional-order Volterra population model via an efficient monotone iterative scheme. By coupling a spectral method with the proposed iterative scheme, the fractional-order integrodiffer- ential equation is solved numerically. The numerical experiments show that the proposed iterative scheme is more efficient than an existing iterative scheme in the literature, the convergence of which is very sensitive to various parameters, including the fractional order of the derivative. The spectral method based on our proposed iterative scheme shows greater flexibility with respect to various parameters. Sufficient conditions are provided to select the initial guess that ensures the quadratic convergence of the quasilinearization scheme. © 2019 Rocky Mountain Mathematics Consortium.
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    Direct and integrated radial functions based quasilinearization schemes for nonlinear fractional differential equations
    (Springer editorial@springerplus.com, 2020) Godavarma, G.; Prashanthi, K.S.; Vijesh, V.
    In this article, two radial basis functions based collocation schemes, differentiated and integrated methods (DRBF and IRBF), are extended to solve a class of nonlinear fractional initial and boundary value problems. Before discretization, the nonlinear problem is linearized using generalized quasilinearization. An interesting proof via generalized monotone quasilinearization for the existence and uniqueness for fractional order initial value problem is given. This convergence analysis also proves quadratic convergence of the generalized quasilinearization method. Both the schemes are compared in terms of accuracy and convergence and it is found that IRBF scheme handles inherent RBF ill-condition better than corresponding DRBF method. Variety of numerical examples are provided and compared with other available results to confirm the efficiency of the schemes. © 2019, Springer Nature B.V.