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Alsaedi, Ahmed
- An Efficient Numerical Method for Solving Chaotic and Non-Chaotic Systems
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Authors
Affiliations
1 Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JO
2 Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, JO
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, SA
1 Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JO
2 Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, JO
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, SA
Source
Journal of the Ramanujan Mathematical Society, Vol 33, No 3 (2018), Pagination: 219-231Abstract
In this article, a numerical scheme based on reproducing kernel Hilbert space method, namely multistep reproducing kernel Hilbert space method (MRKHSM), is devised to solve Chaotic and non-Chaotic systems. This algorithm is applied to Chaotic and non-Chaotic differential equations that model the Lotka-Voltera, Chen, Lorenz and Rossler systems. The numerical results demonstrate that the Multistep reproducing kernel Hilbert space method is reliable method for solving nonlinear problems.
References
- W. Zhou, Y. Xu, H. Lu and L. Pa, On dynamics analysis of a new Chaotic attractor, Physics Letter A., 372 (2008) 5773–5777.
- J. Lu, T. Zhou, G. Chen and S. Zhang, Local bifurcations of the Chen system, International Journal of Bifuraction and Chaos, 12 (2002) no. 10, 2257–2270.
- O. E. Rossler, A equation for continuous Chaos, Physics Letters, 57A (1976) no. 5, 397–398.
- A. Serletis and P. Gegas, Chaos in east European black market exchange rates, Research Economics, 51 (1997) no. 4, 359–385.
- T. Ueta and G. Chen, Bifurcation analysis of Chen’s equation, International Journal of Bifurcation and Chaos, 10 (2000) no. 8, 1917–1931.
- I. Hashim, M. S. M. Noorani, R. Ahmad, S. A. Baker, E. S. Ismail and A.M. Zakaria, Accuracy of the Adomian decomposition method applied to the Lorenz system, Chaos, Solitons and Fractals, 28 (2006) no. 5, 1149–1158.
- A. Ghosh, A. Roy and D. Roy, An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators, Computer Methods in Applied Mechanics and Engineering, 196 (2007) no. 4–6, 1133–1153.
- N. I. Razali, M. S. H. Chowdhurg and W. Asrar, The multistage Adomian decomoposition method for solving Chaotic Lu system, Middle-East Journal of Scientific Research, 13 43–49 (2013).
- M. M. Al-Sawalha, M. S. M. Noorani and I. Hashim, On accuracy of adomian decomposition method for hyperchaotic rossler system, Chaos, Solitons and Fractals, 40 (2009) no. 4, 1801–1807.
- A. K. Alomari, M. S. M. Noorani and R. Nazar, Adaptation of homotopy analysis method for numeric-analytic solution of Chen system, Communications in Nonlinear Science and Numerical Simulation, 14 (2009) no. 5, 2336–2346, .
- A. K. Alomari, M. S. M. Noorani, R. Nazar and C. P. Li, Homotopy analysis method for solving fractional Lorenz system, Communications in Nonlinear Science and Numerical Simulation, 15 (2010) no. 7, 1864–1872.
- M. S. H. Chowdhury and I. Hashim, Application of multistage homotopyperturbation method for the solutions of the Chen system, Nonlinear Analysis: Real World Applications, 10 (2009) no. 1, 381-391. .
- M. S. H. Chowdhury, I. Hashim and S. Momani, The multistage homotopyperturbation method: A powerful scheme for handling the Lorenz system, Chaos, Solitons and Fractals, 40 (2009) no. 4, 1929–1937.
- S. M. Goh, M. S. M. Noorani and I. Hashim, A new application of variational iteration method for the chaotic Rossler system, Chaos, Solitons and Fractals, 42 (2009) no. 3, 1604–1610.
- M. M. Al-Sawalha and M. S. M. Noorani, Application of the differential transformation method for the solution of the hyperchaotic Rossler system, Communications in Nonlinear Science and Numerical Simulation, 14 (2009) no. 4, 1509–1514.
- Z. M. Odibat, C. Bertelle, M. A. Aziz-Alaoui and G. H. E. Duchamp, A multi-step differential transform method and application to non-chaotic or chaotic systems, Computers and Mathematics with Applications, 59 (2010) no. 4, 1462–1472.
- M. M. Al-Sawalha and M. S. M. Noorani, On Solving the Lorenz System by Differential Transformation Method, Chin. Phys. Lett., 25 (2008) no. 4, 1217–1219.
- U. A. M. Roslan, Z. Salleh and A. Kilicman, Solving Zhou’s chaotic system using Euler’s method, Thai Journal of Mathematics, 8 (2010) no. 2, 299–309.
- N. Aronsajn, Theory of reproducing kernels, Transactions of the American Mathematical Society, 68(3) (1950) 337–404.
- F. Geng and M. Cui, A reproducing kernel method for solving nonlocal fractional boundary value problems, Applied Mathematics Letters, 25 (2012) 818–823.
- S. Bushnaq, S. Momani and Y. Zhon, A reproducing Kernel Hilbert space method for solving integro-differential equations of fractional order, Journal of Optimization Theory and Applications (2012).
- M. G. Cui and Y. Z. Lin, Nonlinear numerical analysis in reproducing Kernel Hilbert space, Nova Science, New York (2009).
- Y. Z. Lin and Y. F. Zhou, Solving nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space, Numer. Algor., 52 (2009) 173–186.
- B. Maayah, S. Bushnaq, S. Momani and O. Abu Arqub, Iterative multistep reproducing kernel Hilbert space method for solving strongly nonlinear oscillators, Advances in Mathematical Physics (2014), Article ID 758195.
- F.Geng andM. Cui, Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space, Applied Mathematics and Computation, 192 (2007) 389–398.
- C. Li and M. Cui, The exact solution for solving a class nonlinear operator equations in the reproducing kernel space, Applied Mathematics and Computation, 143 (2003) 393–399.
- W. Jiang and Z. Chen, Solving a system of linear Volterra integral equations using the new reproducing kernel method, Applied Mathematics and Computation, 219 (2013) 10225–10230.
- S. Bushnaq, B. Maayah, S. Momani and A. Alsaidi, A Reproducing Kernel Hilbert space method for solving systems of fractional integro-differential equations, Abstract and Applied Analysis (2014), Article ID 103016.
- O. Abu Arqub, M. Al-Smadi and S. Momani, Applications of reproducing Kernel method for solving nonlinear Fredholm-Voltera integro-differential equations, Abstract and Applied Analysis (2012), Article ID: 839836.
- N. Shawagfeh, O. Abu Arqub and S. Momani, Analytical solution of nonlinear second-order periodic boundary value problem using reproducing Kernel mthod, Journal of Computational Analysis and Applications, 16 (2014) no. 4, 750–762.
- O. Abu Arqub, The reproducing Kernel Algorithm for handling differential algebraic systems of ordinary differential equations, Mathematical Methods in the Applied Sciences, 39(15) (2016).
- L. Yang, H. Li and J. Wang, Solving a system of linear voltera integral equations using the modified reproducing kernel method, Abstract and Applied Analysis (2013), Article ID 196308.