Penyelesaian Persamaan Diferensial Lane Emden Index Nol dengan Metode Simetri Lie
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Abstrak
Salah satu cara menyelesaikan persamaan diferensial orde dua adalah mereduksinya menjadi persamaan diferensial orde satu. Dengan metode simetri Lie persamaan diferensial Lane Emden Index Nol dapat direduksi menjadi persamaan diferensial orde satu yang selanjutnya mudah untuk ditentukan solusinya. Berdasarkan hasil pembahasan, metode simetri Lie dapat digunakan untuk menentukan solusi eksak persamaan diferensial Lane Emden Index Nol.
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Bagian
Applied Mathematics
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Referensi
[1] F. Oliveri, Lie Symmetries of Differential Equations: Classical Results and Recent Contributions, symmetry, Vol. 2 , pp 658 -706, 2010.
[2] S. Mukherjee, B. Roy, P. K. Chaterjee, Solution of Lane Emden Equation by Differential Transform Method. International Journal of Nonlinear Science, Volume 12, Issue 4, pp. 478 - 484, 2011.
[3] Y. Khan, Z. Svoboda, Z. Smarda, Solving certain classes of Lane-Emden type equations using the differential transformation method. Advances in Difference Equations a Springer Open Journal, Volume 174, Issue 1, Pages 1 - 11, 2012.
[4] S. S. Motsa, S. Shateyi, New Analytic Solution to the Lane-Emden Equation of Index 2. Mathematical Problems in Engineering Hindawi Publishing, Pages 1 - 19, 2012.
[5] R. Gilmore, Lie groups, Lie Algebras, and some of their applications. Dover Publications, 2006
[6] I.N. Herstein, Abstract Algebra, 3ed, John Wiley and Son, 1999
[7] J. Starrett, Solving Differential Equations by Symmetry Groups, Jstor, Mathematical Association of America, Volume 114, Issue 9, Pages 778 - 792, 2007.
[8] Z. Martinot, Solutions to Ordinary Differential Equations Using Methods of Symmetry, Paper Zachary Department of Mathematics, University of Washington, 2014.
[9] R. A. Steinhour, The Truth About Lie Symmetries: solving Differential Equations With Symmetry Methods. Senior Independent Study Theses, Department of Mathematics and Computer Science, The College of Wooster, 2013.
[10] M. Singh, On Reduction of Some Differential Equations using Symmetry Methods, Journal of Natural Sciences Research, Volume 5, Issue 3, Pages 44 - 47, 2015.
[2] S. Mukherjee, B. Roy, P. K. Chaterjee, Solution of Lane Emden Equation by Differential Transform Method. International Journal of Nonlinear Science, Volume 12, Issue 4, pp. 478 - 484, 2011.
[3] Y. Khan, Z. Svoboda, Z. Smarda, Solving certain classes of Lane-Emden type equations using the differential transformation method. Advances in Difference Equations a Springer Open Journal, Volume 174, Issue 1, Pages 1 - 11, 2012.
[4] S. S. Motsa, S. Shateyi, New Analytic Solution to the Lane-Emden Equation of Index 2. Mathematical Problems in Engineering Hindawi Publishing, Pages 1 - 19, 2012.
[5] R. Gilmore, Lie groups, Lie Algebras, and some of their applications. Dover Publications, 2006
[6] I.N. Herstein, Abstract Algebra, 3ed, John Wiley and Son, 1999
[7] J. Starrett, Solving Differential Equations by Symmetry Groups, Jstor, Mathematical Association of America, Volume 114, Issue 9, Pages 778 - 792, 2007.
[8] Z. Martinot, Solutions to Ordinary Differential Equations Using Methods of Symmetry, Paper Zachary Department of Mathematics, University of Washington, 2014.
[9] R. A. Steinhour, The Truth About Lie Symmetries: solving Differential Equations With Symmetry Methods. Senior Independent Study Theses, Department of Mathematics and Computer Science, The College of Wooster, 2013.
[10] M. Singh, On Reduction of Some Differential Equations using Symmetry Methods, Journal of Natural Sciences Research, Volume 5, Issue 3, Pages 44 - 47, 2015.