Faculty Publications

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    A radial basis function method for fractional Darboux problems
    (Elsevier Ltd, 2018) Godavarma, C.; Prashanthi, P.; Vijesh, V.A.
    In this paper, a radial basis function (RBF) collocation known as Kansa's method has been extended to solve fractional Darboux problems. The fractional derivatives are described in the Caputo sense. Integration of radial functions that appears due to fractional derivatives have been dealt using Gauss–Jacobi quadrature method. The equation has been linearized using successive approximation. A few test problems have been solved and compared with available solutions. The effect of RBF shape parameter on accuracy and convergence has also been discussed. © 2017 Elsevier Ltd
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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.