SERIES SOLUTION OF EPIDEMIC MODEL

Year 2012, Volume: 2 Issue: 2, 238 - 244, 01.12.2012

Nurettin Dogan Omer Akin

Abstract

The present paper is concerned with the approximate analytic series solution of the epidemic model. In place of the traditional numerical, perturbation or asymtotic methods, Laplace-Adomian decomposition method LADM is employed.To demonstrate the effort of the LADM an epidemic model, which has been worked on recently, has been solved. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Furthermore the results are compared with Fouth Order Runge Method and residual error. After examining the results, we see that LADM is a powerful method for obtaining aproximate solutions to epidemic model.

Keywords

Series solution, Epidemic model, Laplace-Adomian decomposition method, approximate solution, system of nonlinear differential equations

References

• Jordan, D. W. and Smith, P., (1999), Nonlinear Ordinary Differential Equations, third ed., Oxford University Press.
• Biazar, J., (2006), Solution of the epidemic model by Adomian decomposition method, Applied Math- ematics and Computation, 173, 1101-1106.
• Rafei, M., Ganji, D. D. and Daniali, H., (2007), Solution of the epidemic model by homotopy pertur- bation method, Applied Mathematics and Computation, 187, 1056-1062.
• Kiymaz, O., (2009), An Algorithm for Solving Initial Value Problems Using Laplace Adomian De- composition Method, Applied Mathematical Sciences, 3(30), 1453-1459.
• Wazwaz, A. M., (2010), The combined Laplace transform-Adomian decomposition method for han- dling nonlinear Volterra integro-differential equations, Applied Mathematics and Computation, 216, 1304-1309.
• Khuri, S. A., (2001), A Laplace Decomposition Algorithm Applied To A Class Of Nonlinear Differential Equations, Journal of Applied Mathematics, 1:4, 141-155.
• Babolian, E., Biazar, J. and Vahidi, A. R., (2004), A new computational method for Laplace trans- forms by decomposition method, Applied Mathematics and Computation, 150, 841-846.
• Do˘gan, N., (2012), Solution Of The System Of Ordinary Differential Equations By Combined Laplace Transform–Adomian Decomposition Method, Mathematical and Computational Applications, 17(3), 203-211.