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INTERNATIONAL JOURNAL OF ISSN 1312-7586 (print) ISSN 1314-7544 (online) |
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I. H. Abdel-Halim Hassan, V. S. Erturk Applying differential transformation method to the one-dimensional planar Bratu problem Int. Journal of Contemp. Math. Sciences, Vol. 2, 2007, no. 29-32, 1493-1504 http://dx.doi.org/10.12988/ijcms.2007.07157 Copyright © 2007 I. H. Abdel-Halim Hassan and V. S. Erturk. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cited by (46): H.Q. Kafri, S.A. Khuri, Bratu’s problem: A novel approach using fixed-point iterations and Green’s functions, Computer Physics Communications, 198 (2016), 97-104 [CrossRef] Hossein Jafari and Haleh Tajadodi, Electro-spunorganic nanofibers elaboration process investigations using BPs Operational Matrices, Iranian Journal of Mathematical Chemistry, 7 (2016), no. 1, 19-27 [View at Publisher] Randhir Singh, Gnaneshwar Nelakanti and Jitendra Kumar, Approximate solution of two-point boundary value problems using Adomian decomposition method with Green’s function, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 85 (2015), no. 1, 51-61 [CrossRef] Yinghong Xu, Xiangjie Li and Lipu Zhang, The Particle Swarm Shooting Method for Solving the Bratu's Problem** The research is supported by the grant from Natural Science Foundation of Zhejiang Provence No. LY14A010033 and The National Statistical Science Research Project 2014LY050, Journal of Algorithms & Computational Technology, 9 (2015), no. 3, 291-302 [CrossRef] Xiaomin Wang, Xiaojing Liu, Jizeng Wang, Youhe Zhou, A wavelet method for bending of circular plate with large deflection, Acta Mechanica Solida Sinica, 28 (2015), no. 1, 83-90 [CrossRef] W. M. Abd-Elhameed, Y. H. Youssri, E. H. Doha, A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations, Mathematical Sciences, 9 (2015), no. 2, 93-102 [CrossRef] Muhammad Asif Zahoor Raja, Siraj-ul-Islam Ahmad, Numerical treatment for solving one-dimensional Bratu problem using neural networks, Neural Computing and Applications, 24 (2014), no. 3-4, 549-561 [CrossRef] J.M.W. Munganga, J.N. Mwambakana, R. Maritz, T.A. Batubenge, G.M. Moremedi, Introduction of the differential transform method to solve differential equations at undergraduate level, International Journal of Mathematical Education in Science and Technology, 45 (2014), no. 5, 781-794 [CrossRef] M. Asick Ali and P. S. SehikUduman, Mathematical Model Related to Human life Expectancy, International Journal of Mathematics and Statistics Invention (IJMSI), 2 (2014), no. 3, 8-13 [View at Publisher] A. Mohsen, A simple solution of the Bratu problem, Computers & Mathematics with Applications, 67 (2014), no. 1, 26-33 [CrossRef] Adem Kilicman and Omer Altun, On higher-order boundary value problems by using differential transformation method with convolution terms, Journal of the Franklin Institute, 351 (2014), no. 2, 631-642 [CrossRef] XiaoJing Liu, YouHe Zhou, Lei Zhang, JiZeng Wang, Wavelet solutions of Burgers’ equation with high Reynolds numbers, Science China Technological Sciences, 57 (2014), no. 7, 1285-1292 [CrossRef] M. Zarebnia and M. Hoshyar, Solution of Bratu-Type Equation Via Spline Method, Acta Universitatis Apulensis, 37 (2014), 61-72 [View at Publisher] M. Al-Towaiq and Osama Ala'yed, An Efficient Algorithm based on the Cubic Spline for the Solution of Bratu-Type Equation, Journal of Interdisciplinary Mathematics, 17 (2014), no. 5-6, 471-484 [CrossRef] Omar Abu Arqub, Zaer Abo-Hammour, Ramzi Al-Badarneh, Shaher Momani, A reliable analytical method for solving higher-order initial value problems, Discrete Dynamics in Nature and Society, 2013 (2013), 1-12 [CrossRef] Eman S. Alaidarous, Malik Zaka Ullah, Fayyaz Ahmad, A.S. Al-Fhaid, An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs, Journal of Applied Mathematics, 2013 (2013), 1-11 [CrossRef] Lifeng Wang, Yunpeng Ma, Zhijun Meng, Jun Huang, Wavelet Operational Matrix Method for Solving Fractional Integral and Differential Equations of Bratu-Type, CMES: Computer Modeling in Engineering & Sciences, 92 (2013), no. 4, 353-368 [View at Publisher] Mohammad Zarebnia and Zahra Sarvari, New Approach for Numerical Solution of the One-Dimensional Bratu Equation, Thai Journal of Mathematics, 11 (2013), no. 3, 611-621 [View at Publisher] K. R. Raslan and Zain F. Abu Sheer, Comparison Study Between Differential Transform Method and Adomian Decomposition Method for Some Delay Differential Equations, Int. J. Phys. Sci, 8 (2013), no. 17, 744-749 [View at Publisher] E. H. Doha, A. H. Bhrawy, D. Baleanu, R. M. Hafez, Efficient Jacobi-Gauss Collocation Method for Solving Initial Value Problems of Bratu Type, Computational Mathematics and Mathematical Physics, 53 (2013), no. 9, 1292-1302 [CrossRef] A. Kazemi Nasab, Z. Pashazadeh Atabakan and A. Kilicman, An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method, Mathematical Problems in Engineering, 2013 (2013), 1-10 [CrossRef] Muhammad Asif Zahoor Raja, Siraj-ul-Islam Ahmad, Raza Samar, Neural Network Optimized with Evolutionary Computing Technique for Solving the 2-Dimensional Bratu Problem, Neural Computing and Applications, 23 (2013), no. 7-8, 2199-2210 [CrossRef] Xiaojing Liu, Youhe Zhou, Xiaomin Wang, Jizeng Wang, A Wavelet Method for Solving a Class of Nonlinear Boundary Value Problems, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), no. 8, 1939-1948 [CrossRef] Sandile S. Motsa, Precious Sibanda, Some Modifications of the Quasilinearization Method with Higher-Order Convergence for Solving Nonlinear BVPs, Numerical Algorithms, 63 (2013), no. 3, 399-417 [CrossRef] Jalil Rashidinia, Khosro Maleknejad and Narges Taheri, Sinc-Galerkin Method for Numerical Solution of the Bratu’s Problems, Numerical Algorithms, 62 (2013), no. 1, 1-11 [CrossRef] A. Mohsen, On the Integral Solution of the One-Dimensional Bratu Problem, Journal of Computational and Applied Mathematics, 251 (2013), 61-66 [CrossRef] G. Hariharan and P. Pirabaharan, An Efficient Wavelet Method for Initial Value Problems of Bratu-Type Arising in Engineering, Applied Mathematical Sciences, 7 (2013), no. 43, 2121-2130 [View at Publisher] M. A. Hajji and Q. M. Al-Mdallal, Modified Sinc-Galerkin Method for Nonlinear Boundary Value Problems, Journal of Mathematics, 2013 (2013), 1-10 [CrossRef] Yiming Chen, Lu Sun, Lili Liu, Jiaquan Xie, The Chebyshev Wavelet Method for Solving Fractional Integral and Differential Equations of Bratu-type⋆, Journal of Computational Information Systems, 9 (2013), no. 14, 5601-5609 [View at Publisher] A. M. Nazaria and S. Kamali Mahera, Some Properties of Band Matrix and its Application to the Numerical Solution One-Dimensional Bratu's Problem, Journal of Linear and Topological Algebra, 2 (2013), no. 03, 161-167 [View at Publisher] Qiang Li, A Wavelet Method for Solving Nonlinear Time-Dependent Partial Differential Equations, CMES: Computer Modeling in Engineering & Sciences, 94 (2013), no. 3, 225-238 [View at Publisher] Mingxu Yi, Kangwen Sun, Jun Huang, Lifeng Wang, Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets, Journal of Applied Mathematics, 2013 (2013), 1-7 [CrossRef] X. J. Liu, J. Z. Wang and Y. H. Zhou, Wavelet Solution of a Class of Two-Dimensional Nonlinear Boundary Value Problems, CMES: Computer Modelling in Engineering & Science, 92 (2013), no. 5, 493-505 [View at Publisher] S. G. Venkatesh, S. K. Ayyaswamy and S. Raja Balachandar, The Legendre Wavelet Method for Solving Initial Value Problems of Bratu-Type, Computers & Mathematics with Applications, 63 (2012), no. 8, 1287-1295 [CrossRef] Constantin Bota, Bogdan Caruntu and Liviu Bereteu, Approximate Polynomial Solution of a Nonlinear Differential Equation with Applications, Chapter in Dynamical Systems and Methods, Springer New York, 2012, 169-177 [CrossRef] Rahayu, Sugiatno, Bayu Prihandono, Penyelesaian Persamaan Diferensial Biasa Tak Linear Dengan Metode Transformasi Diferensial, Bimaster, 1 (2012), no. 01, 9-14 [View at Publisher] J. Rashidinia and N. Taher, Application of the Sinc Approximation to the Solution of Bratu's Problem, International Journal of Mathematical Modelling & Computations, 2 (2012), no. 3, 239-246 [View at Publisher] Hal Finkel, An Iterated, Multipoint Differential Transform Method for Numerically Evolving Partial Differential Equation Initial-Value Problems, Computational Science & Discovery, 5 (2012), no. 1, 1-19 [CrossRef] S. Abbasbandy, M. S. Hashemi and Chein-Shan Liu, The Lie-Group Shooting Method for Solving the Bratu Equation, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), no. 11, 4238-4249 [CrossRef] John P. Boyd, One-Point Pseudospectral Collocation for the One-Dimensional Bratu Equation, Applied Mathematics and Computation, 217 (2011), no. 12, 5553-5565 [CrossRef] S. Abbasbandy, M.S. Hashemi, Chein-Shan Liu, The Lie-Group Shooting Method for Solving the Bratu Equation, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), no. 11, 4238-4249 [CrossRef] Hikmet Caglar, Nazan Caglar, Mehmet Ozer, Antonios Valarıstos, Antonios N. Anagnostopoulos, B-Spline Method for Solving Bratu's Problem, International Journal of Computer Mathematics, 87 (2010), no. 8, 1885-1891 [CrossRef] R. Jalilian, Non-Polynomial Spline Method for Solving Bratu's Problem, Computer Physics Communications, 181 (2010), no. 11, 1868-1872 [CrossRef] Jalil Rashidinia and Reza Jalilian, Spline Solution of Two Point Boundary Value Problems, Appl. Comput. Math, 9 (2010), no. 2, 258-266 [View at Publisher] S. G. Venkatesh, S. K. Ayyaswamy and G. Hariharan, Haar Wavelet Method for solving Initial and Boundary Value Problems of Bratu-Type, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 4 (2010), no. 7, 914-917 [View at Publisher] Hikmet Caglar, Nazan Caglar, Mehmet Ozer, Antonios Valaristos, Amalia N. Miliou, Antonios N. Anagnostopoulos, Dynamics of the Solution of Bratu’s Equation, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), no. 12, e672-e678 [CrossRef]
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