Numerical investigations to design a novel model based on the fifth order system of Emden–Fowler equations

Theoretical and Applied Mechanics Letters - Tập 10 - Trang 333-342 - 2020
Zulqurnain Sabir1, Mehmet Giyas Sakar2, Manshuk Yeskindirova3, Onur Saldir1
1Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
2Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, Van, Turkey
3Department of Translation Theory and Practice, L. N. Gumilyov Eurasian National University, Kazakhstan

Tài liệu tham khảo

Richardson, 1921 Sabir, 2020, Novel design of Morlet wavelet neural network for solving second order Lane-Emden equation, Mathematics and Computers in Simulation, 172, 1, 10.1016/j.matcom.2020.01.005 Davis, 1962 Li, 2017, Oscillation criteria for second-order superlinear Emden–Fowler neutral differential equations, Monatshefte für Mathematik, 184, 489, 10.1007/s00605-017-1039-9 Sabir, 2020, Intelligence computing approach for solving second order system of Emden–Fowler model, Journal of Intelligent & Fuzzy Systems, 38, 1, 10.3233/JIFS-179813 Mandelzweig, 2001, Quasi linearization approach to nonlinear problems in physics with application to nonlinear ODEs, Computer Physics Communications, 141, 268, 10.1016/S0010-4655(01)00415-5 Luo, 2016, Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities, Communications in Mathematical Physics, 347, 657, 10.1007/s00220-016-2753-1 Flockerzi, 2011, On coupled Lane-Emden equations arising in dusty fluid models, Journal of Physics: Conference Series, 268 Rach, 2014, Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method, Journal of Mathematical Chemistry, 52, 255, 10.1007/s10910-013-0260-6 Džurina, 2020, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293, 1, 10.1002/mana.201800196 Khan, 2015, Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory, Connection Science, 27, 377, 10.1080/09540091.2015.1092499 Ramos, 2003, Linearization methods in classical and quantum mechanics, Computer Physics Communications, 153, 199, 10.1016/S0010-4655(03)00226-1 Bhrawy, 2014, An efficient collocation method for a class of boundary value problems arising in mathematical physics and geometry, Abstract and Applied Analysis, 10.1155/2014/425648 Dehghan, 2008, Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method, Progress in Electromagnetics Research, 78, 361, 10.2528/PIER07090403 Taghavi, 2013, A solution to the Lane–Emden equation in the theory of stellar structure utilizing the Tau method, Mathematical Methods in the Applied Sciences, 36, 1240, 10.1002/mma.2676 Ghergu, 2007, On a class of singular Gierer–Meinhardt systems arising in morphogenesis, Comptes Rendus Mathématique, 344, 163, 10.1016/j.crma.2006.12.008 Radulescu, 2012, Combined effects in nonlinear problems arising in the study of anisotropic continuous media, Nonlinear Analysis: Theory, Methods and Applications, 75, 1524 Shawagfeh, 1993, Non-perturbative approximate solution for Lane–Emden equation, Journal of Mathematical Physics, 34, 4364, 10.1063/1.530005 Li, 2017, On asymptotic behavior of solutions to higher-order sublinear Emden–Fowler delay differential equations, Applied Mathematics Letters, 67, 53, 10.1016/j.aml.2016.11.007 Parand, 2004, Rational Legendre approximation for solving some physical problems on semi-infinite intervals, Physica Scripta, 69, 353, 10.1238/Physica.Regular.069a00353 Liao, 2003, A new analytic algorithm of Lane–Emden type equations, Applied Mathematics and Computation, 142, 1, 10.1016/S0096-3003(02)00943-8 Bender, 1989, A new perturbative approach to nonlinear problems, Journal of Mathematical Physics, 30, 1447, 10.1063/1.528326 Nouh, 2004, Accelerated power series solution of polytropic and isothermal gas spheres, New Astronomy, 9, 467, 10.1016/j.newast.2004.02.003 Sabir, 2019, Stochastic numerical approach for solving second order nonlinear singular functional differential equation, Applied Mathematics and Computation, 363, 10.1016/j.amc.2019.124605 Sabir, 2020, Neuro-swarm intelligent computing to solve the second-order singular functional differential model, The European Physical Journal Plus, 135, 474, 10.1140/epjp/s13360-020-00440-6 Sabir, 2020, Design of neuro-swarming-based heuristics to solve the third-order nonlinear multisingular Emden–Fowler equation, The European Physical Journal Plus, 135, 1, 10.1140/epjp/s13360-020-00424-6 Adel, 2020, Solving a new design of nonlinear second-order Lane–Emden pantograph delay differential model via Bernoulli collocation method, The European Physical Journal Plus, 135, 427, 10.1140/epjp/s13360-020-00449-x Sabir, 2020, On a new model based on third-order nonlinear multisingular functional differential equations, Mathematical Problems in Engineering, 2020, 10.1155/2020/1683961 Sabir, 2020, A neuro-swarming intelligence based computing for second order singular periodic nonlinear boundary value problems, Front. Phys., 10.3389/fphy.2020.00224 He, 1997, Variational iteration method for delay differential equations, Communications in Nonlinear Science and Numerical Simulation, 2, 235, 10.1016/S1007-5704(97)90008-3 He, 1998, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering, 167, 69, 10.1016/S0045-7825(98)00109-1 He, 1999, Variational iteration method–a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics, 34, 699, 10.1016/S0020-7462(98)00048-1 Inokuti, 1978, General use of the Lagrange multiplier in nonlinear mathematical physics, 156 Wazwaz, 2011, The variational iteration method for solving systems of equations of Emden–Fowler type, International Journal of Computer Mathematics, 88, 3406, 10.1080/00207160.2011.587513 Sabir, 2014, Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique, International Journal of Industrial Engineering Computations, 5, 431, 10.5267/j.ijiec.2014.3.004 Umar, 2019, Unsupervised constrained neural network modeling of boundary value corneal model for eye surgery, Applied Soft Computing, 85, 10.1016/j.asoc.2019.105826 Umar, 2019, Intelligent computing for numerical treatment of nonlinear prey–predator models, Applied Soft Computing, 80, 506, 10.1016/j.asoc.2019.04.022 Raja, 2018, A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head, The European Physical Journal Plus, 133, 364, 10.1140/epjp/i2018-12153-4 Sabir, 2018, Neuro-heuristics for nonlinear singular Thomas-Fermi systems, Applied Soft Computing, 65, 152, 10.1016/j.asoc.2018.01.009 Raja, 2019, Numerical solution of doubly singular nonlinear systems using neural networks-based integrated intelligent computing, Neural Computing and Applications, 31, 793, 10.1007/s00521-017-3110-9 Raja, 2015, Design of stochastic solvers based on genetic algorithms for solving nonlinear equations, Neural Computing and Applications, 26, 1, 10.1007/s00521-014-1676-z