Computational heuristics for Troesch’s Problem in Plasma Physics
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DOI:
https://doi.org/10.59287/ijanser.1503Keywords:
Non-Linear Systems, Genetic Algorithm, Exponential Collocation, Singular Model, Troesch’s ProblemAbstract
Exponential Collocation Genetic Algorithm (ECGA) approach has been developed and analyzed for fast computation of hyperbolic sine nonlinear Troesch’s problem which arises in the confinement of plasma. The governing equation is converted to an optimization problem by formulating the Fitness function in terms of an exponential basis. The problem is solved for three scenarios of Troesch’s parameters of 0.5, 1, and 2 respectively. The stability of the solutions has been investigated for multiple independent runs. The results obtained in this work are in good agreement with the already published with enhanced stability and fast convergence. The developed technique is a simple and reliable method for the solution of hyperbolic sine nonlinear Troesch’s problem.
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References
Weibel, E.S. (1959) On the confinement of plasma by magnetostatic fields. The Physics of Fluids,. 2(1):52-56.
Gidaspow, D., and Baker, B.S. (1973) A model for discharge of storage batteries. Journal of the Electrochemical Society, 120(8): 1005.
Roberts, S., and Shipman, J. (1976) On the closed form solution of Troesch's problem. Journal of Computational Physics, 21(3): 291-304.
El-Gamel, M., (2013) Numerical solution of Troesch’s problem by sinc-collocation method. Applied Mathematics, 4(4): 707-712.
Feng, X., Mei, L., and He, G. (2007) An efficient algorithm for solving Troesch’s problem. Applied Mathematics and Computation, 189(1): 500-507.
Temimi, H., (2012) A discontinuous Galerkin finite element method for solving the Troesch’s problem. Applied Mathematics and Computation, 219(2): 521-529.
Erdogan, U., and Ozis, T. (2011) A smart nonstandard finite difference scheme for second order nonlinear boundary value problems. Journal of Computational Physics, 230(17): 6464-6474.
Chin, R., and Krasny, R. (1983) A hybrid asymptotic-finite element method for stiff two-point boundary value problems. SIAM Journal on
Scientific and statistical Computing, 4(2): 229-243.
Momani, S., Abuasad, S., and Odibat, Z. (2006) Variational iteration method for solving nonlinear boundary value problems. Applied Mathematics and Computation, 183(2): 1351-1358.
Raja, M. A. Z., Shah, F. H., Tariq, M., & Ahmad, I. (2018) Design of artificial neural network models optimized with sequential quadratic programming to study the dynamics of nonlinear Troesch’s problem arising in plasma physics. Neural Computing and Applications, 29(6): 83-109.
Raja, M.A.Z., (2013) Unsupervised neural networks for solving Troesch's problem. Chinese Physics B,. 23(1): 018903.
Majeed, K., Masood, Z., Samar, R., & Raja, M. A. Z. (2017). A genetic algorithm optimized Morlet wavelet artificial neural network to study the dynamics of nonlinear Troesch’s system. Applied Soft Computing, 56 : 420-435.
Raja, M. A. Z., Zameer, A., Khan, A. U., and Wazwaz, A. M. (2016). A new numerical approach to solve Thomas–Fermi model of an atom using bioinspired heuristics integrated with sequential quadratic programming. SpringerPlus, 5(1): 1-22.
Gutierrez-Navarro, D., and Lopez-Aguayo, S. (2018). Solving ordinary differential equations using genetic algorithms and the Taylor series matrix method. Journal of physics communications, 2(11): 115010.
Sabir, M. M. (2018) Electrohydrodynamic flow solution in ion drag in a circular cylindrical conduit using hybrid neural network and genetic algorithm. Kuwait Journal of Science, 45(1).
Sabir, Z., Wahab, H. A., and Guirao, J. L. (2022). A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models. Mathematical Biosciences and Engineering, 19(1): 663-687.
Yousaf, N., uz Zaman, W., Zameer, A., Mirza, S. M., & Nasir, R. (2022). Computational heuristics for solving nonlinear singular ThomasFermi equationwith genetic exponential collocation algorithm. The European Physical Journal Plus, 137(7): 782.
Haldurai, L., Madhubala, T., & Rajalakshmi, R. (2016). A study on genetic algorithm and its applications. International Journal of Computer Sciences and Engineering, 4(10), 139.
Deeba, E., Khuri, S. A., and Xie, S. (2000). An algorithm for solving boundary value problems. Journal of Computational Physics, 159(2):
-138.
