Prasantha Bharathi Dhandapani¹, Dumitru Baleanu^2,3,4,*, Jayakumar Thippan¹, Vinoth Sivakumar¹

Computer Systems Science and Engineering, Vol.37, No.3, pp. 331-346, 2021, DOI:10.32604/csse.2021.015619 - 08 March 2021

Abstract In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people’s disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth… More >

T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 171-204, 2012, DOI:10.3970/cmes.2012.084.171

Abstract In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. Five types of compact stencils - 3-node and 5-node for 1D problems and 5×5-node, 13-node and 3×3 -node for 2D problems - are implemented. In the case of 3-node stencil and 3×3-node stencil, nodal values of the first derivative(s) of the field variable are treated as additional unknowns (i.e. 2 unknowns per node for 3-node stencil and 3 unknowns per node for 3×3-node stencil). The integration constants… More >

James D.Turner, Manoranjan Majji, John L. Junkins

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.1, pp. 11-12, 2011, DOI:10.3970/icces.2011.016.011

Abstract Modeling uncertainty for nonlinear systems is often handled by developing a mathematical model, defining suitable parameters, establishing suitable initial conditions and numerically integrating the system response in order to study the behavior of the system. The potential range of behaviors that can be realized is assessed by varying the model parameters, integrating the response, and recording the changes in the system behaviors. In theory this process is straightforward for implementing. The only potential barrier to carrying out the repeated integrations of the system dynamics is the availability of powerful computer resources that can provide the… More >

Hung-Chang Lee¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.041.001

Abstract The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They More >