A note on the multi-stage spectral relaxation method for chaos control and synchronization
- Dlamini, Phumlani Goodwill, Khumalo, Melusi, Motsa, Sandile Sydney
- Authors: Dlamini, Phumlani Goodwill , Khumalo, Melusi , Motsa, Sandile Sydney
- Date: 2014
- Subjects: Multistage spectral relaxation method , Chaos control and synchronization , Numerical methods
- Type: Article
- Identifier: uj:5430 , http://hdl.handle.net/10210/12049
- Description: In this study, we present and apply a new, accurate and easy to implement numerical method to realize and verify the synchronization between two identical chaotic Lorenz, Genesio-Tesi, Rössler, Chen and Rikitake systems. The proposed method is called the multi-stage spectral relaxation method (MSRM). We utilize the active control technique for the synchronization of these systems. To illustrate the effectiveness of the method, simulation results are presented and compared with results obtained using the Runge-Kutta (4, 5) based MATLAB solver, ode45.
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- Authors: Dlamini, Phumlani Goodwill , Khumalo, Melusi , Motsa, Sandile Sydney
- Date: 2014
- Subjects: Multistage spectral relaxation method , Chaos control and synchronization , Numerical methods
- Type: Article
- Identifier: uj:5430 , http://hdl.handle.net/10210/12049
- Description: In this study, we present and apply a new, accurate and easy to implement numerical method to realize and verify the synchronization between two identical chaotic Lorenz, Genesio-Tesi, Rössler, Chen and Rikitake systems. The proposed method is called the multi-stage spectral relaxation method (MSRM). We utilize the active control technique for the synchronization of these systems. To illustrate the effectiveness of the method, simulation results are presented and compared with results obtained using the Runge-Kutta (4, 5) based MATLAB solver, ode45.
- Full Text:
Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy
- Awad, Faiz G., Motsa, Sandile, Khumalo, Melusi
- Authors: Awad, Faiz G. , Motsa, Sandile , Khumalo, Melusi
- Date: 2014
- Subjects: Spectral relaxation method , Arrhenius activation energy , Partial differential equations
- Type: Article
- Identifier: uj:5437 , http://hdl.handle.net/10210/12594
- Description: In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.
- Full Text:
- Authors: Awad, Faiz G. , Motsa, Sandile , Khumalo, Melusi
- Date: 2014
- Subjects: Spectral relaxation method , Arrhenius activation energy , Partial differential equations
- Type: Article
- Identifier: uj:5437 , http://hdl.handle.net/10210/12594
- Description: In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.
- Full Text:
Spectral relaxation method and spectral quasilinearization method for solving unsteady boundary layer flow problems
- Motsa, Sandile Sydney, Dlamini, Phumlani Goodwill, Khumalo, Melusi
- Authors: Motsa, Sandile Sydney , Dlamini, Phumlani Goodwill , Khumalo, Melusi
- Date: 2014
- Subjects: Nonlinear partial differential equations , Spectral quasilinearization method , Partial differential equations , Spectral relaxation method
- Type: Article
- Identifier: uj:5431 , http://hdl.handle.net/10210/12050
- Description: Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.
- Full Text:
- Authors: Motsa, Sandile Sydney , Dlamini, Phumlani Goodwill , Khumalo, Melusi
- Date: 2014
- Subjects: Nonlinear partial differential equations , Spectral quasilinearization method , Partial differential equations , Spectral relaxation method
- Type: Article
- Identifier: uj:5431 , http://hdl.handle.net/10210/12050
- Description: Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.
- Full Text:
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