Browsing by Author "Parumasur, Nabendra."

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A comparative study of collocation methods for the numerical solution of differential equations.
(2008) Kajotoni, Margaret Modupe.; Parumasur, Nabendra.; Singh, Pravin.
The collocation method for solving ordinary differential equations is examined. A detailed comparison with other weighted residual methods is made. The orthogonal collocation method is compared to the collocation method and the advantage of the former is illustrated. The sensitivity of the orthogonal collocation method to different parameters is studied. Orthogonal collocation on finite elements is used to solve an ordinary differential equation and its superiority over the orthogonal collocation method is shown. The orthogonal collocation on finite elements is also used to solve a partial differential equation from chemical kinetics. The results agree remarkably with those from the literature.
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.
The application of the multigrid algorithm to the solution of stiff ordinary differential equations resulting from partial differential equations.
(1992) Parumasur, Nabendra.; Mika, Janusz R.
We wish to apply the newly developed multigrid method [14] to the solution of ODEs resulting from the semi-discretization of time dependent PDEs by the method of lines. In particular, we consider the general form of two important PDE equations occuring in practice, viz. the nonlinear diffusion equation and the telegraph equation. Furthermore, we briefly examine a practical area, viz. atmospheric physics where we feel this method might be of significance. In order to offer the method to a wider range of PC users we present a computer program, called PDEMGS. The purpose of this program is to relieve the user of much of the expensive and time consuming effort involved in the solution of nonlinear PDEs. A wide variety of examples are given to demonstrate the usefulness of the multigrid method and the versatility of PDEMGS.
Chebyshev spectral and pseudo-spectral methods in unbounded domains.
(2015) Govinder, Saieshan.; Shindin, Sergey Konstantinovich.; Parumasur, Nabendra.
Chebyshev type spectral methods are widely used in numerical simulations of PDEs posed in unbounded domains. Such methods have a number of important computational advantages. In particular, they admit very efficient practical implementation. However, the stability and convergence analysis of these methods require deep understanding of approximation properties of the underlying functional basis. In this project, we deal with Chebyshev spectral and pseudo-spectral methods in unbounded domains. The first part of the project deals with theoretical analysis of Chebyshev-type spectral projection and interpolation operators in Bessel potential spaces. In the second part, we provide rigorous analyses of Chebyshev-type pseudo-spectral (collocation) scheme applied to the nonlinear Schrodinger equation. The project is concluded with several numerical experiments.
Numerical solution of the Klein-Gordon equation in an unbounded domain.
(2018) Lukumon, Gafari Abiodun.; Parumasur, Nabendra.; Shindin, Sergey Konstantinovich.
Abstract available in PDF file.
Spectral methods for nonlocal wave problems.
(2019) Pillay, Marc.; Shindin, Sergey Konstantinovich.; Parumasur, Nabendra.
Abstract available in PDF.