Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 87, 2010 - Issue 8
Submit an article Journal homepage
447
Views
84
CrossRef citations to date
0
Altmetric
Section B

B-spline method for solving Bratu's problem

Hikmet Caglar Department of Mathematics-Computer, Istanbul Kultur University, TR-34156
,
Nazan Caglar Department of Business Administration, Istanbul Kultur University, TR-34156Correspondence[email protected]
,
Mehmet Özer Department of Physics, Istanbul Kultur University, TR-34156
,
Antonios Valarıstos Department of Informatics, Aristotle University of Thessaloniki, GR-54124
&
Antonios N. Anagnostopoulos Department of Physics, Aristotle University of Thessaloniki, GR-54124
Pages 1885-1891 | Received 27 May 2008, Accepted 20 Sep 2008, Published online: 15 Jul 2009

Citations (84)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (4)

Osama Ala’yed, Belal Batiha, Raft Abdelrahim & Ala’a Jawarneh. (2019) On the numerical solution of the nonlinear Bratu type equation via quintic B-spline method. Journal of Interdisciplinary Mathematics 22:4, pages 405-413.
Read now
Pradip Roul & Kiran Thula. (2019) A fourth-order B-spline collocation method and its error analysis for Bratu-type and Lane–Emden problems. International Journal of Computer Mathematics 96:1, pages 85-104.
Read now
Yu-Lan Wang, Dan Tian, Shu-Hong Bao & Zhi-Yuan Li. (2017) Using the iterative reproducing kernel method for solving a class of nonlinear fractional differential equations. International Journal of Computer Mathematics 94:12, pages 2558-2572.
Read now
Muhammad Asif Zahoor Raja. (2014) Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP. Connection Science 26:3, pages 195-214.
Read now

Articles from other publishers (80)

H. Temimi & M. Ben-Romdhane. (2024) A highly accurate discontinuous Galerkin method for solving nonlinear Bratu's problem. Alexandria Engineering Journal 95, pages 50-58.
Crossref
Tugal Zhanlav, Balt Batgerel, Khuder Otgondorj, Dashnamjil Buyantogtokh, Vandandoo Ulziibayar & Renchin-Ochir Mijiddorj. (2024) Higher-Order Finite-Difference Schemes for Nonlinear Two-Point Boundary Value Problems. Journal of Mathematical Sciences 279:6, pages 850-865.
Crossref
A.O. Adewumi, A.A. Aderogba, S.O. Akindeinde, O.O. Fabelurin & R.S. Lebelo. (2024) Finite difference spectral collocation schemes for the solutions of boundary value problems. Heliyon 10:1, pages e23453.
Crossref
H. Temimi, M. Ben-Romdhane & M. Baccouch. (2024) An efficient accurate scheme for solving the three-dimensional Bratu-type problem. Applied Mathematics and Computation 461, pages 128316.
Crossref
Junaid Ahmad, Muhammad Arshad, Kifayat Ullah & Zhenhua Ma. (2023) Numerical solution of Bratu’s boundary value problem based on Green’s function and a novel iterative scheme. Boundary Value Problems 2023:1.
Crossref
Saurabh Tomar, Soniya Dhama, Higinio Ramos & Mehakpreet Singh. (2023) An efficient technique based on Green’s function for solving two-point boundary value problems and its convergence analysis. Mathematics and Computers in Simulation 210, pages 408-423.
Crossref
Tumurkhuyag Badarch & Batgerel Balt. (2023) Artificial Neural Network Method for Solving of Bratu’s Problem. Journal of Institute of Mathematics and Digital Technology 4:1, pages 25-33.
Crossref
Ruixue Sun & Yufeng Xu. (2023) Numerical solutions of Gelfand equation in steady combustion process. Applied Mathematics and Computation 441, pages 127674.
Crossref
Mohammed Al-Smadi, Shaher Momani, Nadir Djeddi, Ahmad El-Ajou & Zeyad Al-Zhour. (2022) Adaptation of reproducing kernel method in solving Atangana–Baleanu fractional Bratu model. International Journal of Dynamics and Control 11:1, pages 136-148.
Crossref
Jyoti & Mandeep Singh. (2022) An iterative technique based on HPM for a class of one dimensional Bratu’s type problem. Mathematics and Computers in Simulation 200, pages 50-64.
Crossref
Pradip Roul & V.M.K. Prasad Goura. (2022) A high‐order efficient technique and its convergence analysis for Bratu‐type and Lane‐Emden‐type problems. Mathematical Methods in the Applied Sciences 45:9, pages 5215-5233.
Crossref
Zhi Liu, Tienmo Shih & Zhong Chen. (2021) Robustness of convergence demonstrated byparametric-guiding andcomplex-root-tunneling algorithms for Bratu’s problem. International Journal of Numerical Methods for Heat & Fluid Flow 32:6, pages 2070-2086.
Crossref
Harendra Singh. (2021) Solving a class of local and nonlocal elliptic boundary value problems arising in heat transfer. Heat Transfer 51:2, pages 1524-1542.
Crossref
Ram Kishun Lodhi, Saud Fahad Aldosary, Kottakkaran Sooppy Nisar & Ateq Alsaadi. (2022) Numerical solution of non-linear Bratu-type boundary value problems via quintic B-spline collocation method. AIMS Mathematics 7:4, pages 7257-7273.
Crossref
Pooja Khandelwal, Arshad Khan & Talat Sultana. (2021) Discrete cubic spline technique for solving one-dimensional Bratu’s problem. Asian-European Journal of Mathematics 15:01.
Crossref
Swati, Mandeep Singh & Karanjeet Singh. (2021) An advancement approach of Haar wavelet method and Bratu-type equations. Applied Numerical Mathematics 170, pages 74-82.
Crossref
Harendra Singh. (2021) Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems. International Journal of Nonlinear Sciences and Numerical Simulation 0:0.
Crossref
M. A. Mehrpouya & R. Salehi. (2021) A numerical scheme based on the collocation and optimization methods for accurate solution of sensitive boundary value problems. The European Physical Journal Plus 136:9.
Crossref
G. Swaminathan, G. Hariharan, V. Selvaganesan & S. Bharatwaja. (2021) A new spectral collocation method for solving Bratu-type equations using Genocchi polynomials. Journal of Mathematical Chemistry 59:8, pages 1837-1850.
Crossref
Ghulam Mustafa, Syeda Tehmina Ejaz, Sabila Kouser, Shafqat Ali & Muhammad Aslam. (2021) Subdivision Collocation Method for One-Dimensional Bratu’s Problem. Journal of Mathematics 2021, pages 1-8.
Crossref
S.N. Jator, D.C. Mayo & M.T. Omojola. (2021) Block Hybrid Third Derivative Nyström type Method for Bratu’s equation. Mathematics and Computers in Simulation 185, pages 256-271.
Crossref
Ashfaq Ahmad, Muhammad Sulaiman, Abdulah Jeza Aljohani, Ahmad Alhindi & Hussam Alrabaiah. (2021) Design of an efficient algorithm for solution of Bratu differential equations. Ain Shams Engineering Journal 12:2, pages 2211-2225.
Crossref
Nasibeh Karamollahi, Ghasem Barid Loghmani & Mohammad Heydari. (2021) A computational method to find dual solutions of the one-dimensional Bratu problem. Journal of Computational and Applied Mathematics 388, pages 113309.
Crossref
BAHRAM AGHELI. (2021) Approximate Solution of Bratu Differential Equations Using Trigonometric Basic Functions. Kragujevac Journal of Mathematics 45:02, pages 203-214.
Crossref
Adrian PatruselIoan A. RusMarcel Adrian Serban. (2021) Theoretical and numerical considerations on Bratu-type problems. Studia Universitatis Babes-Bolyai Matematica 66:1, pages 29-46.
Crossref
Yongjun Xu. (2021) A Novel Numerical-Analytical Approach Using FIPIM for Critical Eigenvalue Investigation Meanwhile Solving the Corresponding Bratu's Problem. International Journal of Applied and Computational Mathematics 7:1.
Crossref
You-He ZhouYou-He Zhou. 2021. Wavelet Numerical Method and Its Applications in Nonlinear Problems. Wavelet Numerical Method and Its Applications in Nonlinear Problems 223 248 .
M. A. Rufai & Higinio Ramos. (2020) Numerical solution of Bratu’s and related problems using a third derivative hybrid block method. Computational and Applied Mathematics 39:4.
Crossref
Randhir Singh. (2020) An iterative technique for solving a class of local and nonlocal elliptic boundary value problems. Journal of Mathematical Chemistry 58:9, pages 1874-1894.
Crossref
Pradip Roul & V. M. K. Prasad Goura. (2020) A Bessel collocation method for solving Bratu’s problem. Journal of Mathematical Chemistry 58:8, pages 1601-1614.
Crossref
A. Kouibia, M. Pasadas & R. Akhrif. (2020) A variational method for solving two-dimensional Bratu’s problem. Numerical Algorithms 84:4, pages 1589-1599.
Crossref
H. Temimi, M. Ben-Romdhane, M. Baccouch & M.O. Musa. (2020) A two-branched numerical solution of the two-dimensional Bratu's problem. Applied Numerical Mathematics 153, pages 202-216.
Crossref
Higinio Ramos & M. A. Rufai. (2019) Numerical solution of boundary value problems by using an optimized two-step block method. Numerical Algorithms 84:1, pages 229-251.
Crossref
Pradip Roul & V. M. K. Prasad Goura. (2020) A sixth order optimal B-spline collocation method for solving Bratu’s problem. Journal of Mathematical Chemistry 58:5, pages 967-988.
Crossref
Sevin Gümgüm, Nurcan Baykuş-savaşaneril, Ömür Kıvanç Kürkçü & Mehmet Sezer. (2020) Lucas Polynomial Approach for Second Order Nonlinear Differential Equations. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24:1, pages 230-236.
Crossref
Xiaolong Ma, Bo Wu, Jiaohua Zhang & Xi Shi. (2019) A new numerical scheme with Wavelet–Galerkin followed by spectral deferred correction for solving string vibration problems. Mechanism and Machine Theory 142, pages 103623.
Crossref
Mohamad Adabitabar Firozja & Bahram Agheli. (2019) Approximate method for solving strongly fractional nonlinear problems using fuzzy transform. Nonlinear Engineering 9:1, pages 72-80.
Crossref
Saurabh Tomar & R.K. Pandey. (2019) An efficient iterative method for solving Bratu-type equations. Journal of Computational and Applied Mathematics 357, pages 71-84.
Crossref
Mina B. Abd-el-Malek, Amr Abdelrazek, Mohammed Ghazy & Gehad Gamal. (2019) A modified perturbation solution to the one-dimensional Bratu problem. Applied Mathematics and Computation 354, pages 296-304.
Crossref
Pradip Roul, Kiran Thula & VMK Prasad Goura. (2019) An optimal sixth‐order quartic B‐spline collocation method for solving Bratu‐type and Lane‐Emden–type problems. Mathematical Methods in the Applied Sciences 42:8, pages 2613-2630.
Crossref
Mohamed Ben-Romdhane, Helmi Temimi & Mahboub Baccouch. (2019) An iterative finite difference method for approximating the two-branched solution of Bratu's problem. Applied Numerical Mathematics 139, pages 62-76.
Crossref
Aisarul Hassan, Siraj-ul-Islam Ahmad, Muhammad Kamran, Ahsan Illahi & Raja Muhammad Asif Zahoor. (2019) Design of cascade artificial neural networks optimized with the memetic computing paradigm for solving the nonlinear Bratu system. The European Physical Journal Plus 134:3.
Crossref
Pradip Roul & Harshita Madduri. (2018) An optimal iterative algorithm for solving Bratu-type problems. Journal of Mathematical Chemistry 57:2, pages 583-598.
Crossref
Fateme Ghomanjani & Stanford Shateyi. (2019) A new approach for solving Bratu’s problem. Demonstratio Mathematica 52:1, pages 336-346.
Crossref
Ali Ümit KeskinAli Ümit Keskin. 2019. Boundary Value Problems for Engineers. Boundary Value Problems for Engineers 167 258 .
Mojtaba Hajipour, Amin Jajarmi & Dumitru Baleanu. (2017) On the accurate discretization of a highly nonlinear boundary value problem. Numerical Algorithms 79:3, pages 679-695.
Crossref
Mehmet Giyas Sakar, Onur Saldır & Ali Akgül. (2018) Numerical Solution of Fractional Bratu Type Equations with Legendre Reproducing Kernel Method. International Journal of Applied and Computational Mathematics 4:5.
Crossref
E. Keshavarz, Y. Ordokhani & M. Razzaghi. (2018) The Taylor wavelets method for solving the initial and boundary value problems of Bratu-type equations. Applied Numerical Mathematics 128, pages 205-216.
Crossref
A. Akgül & M. Giyas Sakar. A new application of reproducing kernel Hilbert space method. A new application of reproducing kernel Hilbert space method.
S.N. Jator & V. Manathunga. (2018) Block Nyström type integrator for Bratu’s equation. Journal of Computational and Applied Mathematics 327, pages 341-349.
Crossref
M. H. Noori Skandari & M. Ghaznavi. (2017) Chebyshev Pseudo-Spectral Method for Bratu’s Problem. Iranian Journal of Science and Technology, Transactions A: Science 41:4, pages 913-921.
Crossref
Xiaojing Liu, Jizeng Wang & Youhe Zhou. (2017) A space–time fully decoupled wavelet Galerkin method for solving a class of nonlinear wave problems. Nonlinear Dynamics 90:1, pages 599-616.
Crossref
Ola Ragb, L.F. Seddek & M.S. Matbuly. (2017) Iterative differential quadrature solutions for Bratu problem. Computers & Mathematics with Applications 74:2, pages 249-257.
Crossref
Zaheer Masood, Khalid Majeed, Raza Samar & Muhammad Asif Zahoor Raja. (2017) Design of Mexican Hat Wavelet neural networks for solving Bratu type nonlinear systems. Neurocomputing 221, pages 1-14.
Crossref
Muhammad Asif Zahoor Raja, Raza Samar, Eman S. Alaidarous & Elyas Shivanian. (2016) Bio-inspired computing platform for reliable solution of Bratu-type equations arising in the modeling of electrically conducting solids. Applied Mathematical Modelling 40:11-12, pages 5964-5977.
Crossref
Nilima Das, Randhir Singh, Abdul-Majid Wazwaz & Jitendra Kumar. (2015) An algorithm based on the variational iteration technique for the Bratu-type and the Lane–Emden problems. Journal of Mathematical Chemistry 54:2, pages 527-551.
Crossref
Bilal Shoaib, Ijaz Mansoor Qureshi, Wasim Khan, Shafqat Ullah Khan & Abdul Basit. (2016) Numerical solution of nonlinear Boundary value problems in kernel space. Numerical solution of nonlinear Boundary value problems in kernel space.
H.Q. Kafri & S.A. Khuri. (2016) Bratu’s problem: A novel approach using fixed-point iterations and Green’s functions. Computer Physics Communications 198, pages 97-104.
Crossref
H. Temimi & M. Ben-Romdhane. (2016) An iterative finite difference method for solving Bratu’s problem. Journal of Computational and Applied Mathematics 292, pages 76-82.
Crossref
Natalia Romero. (2015) Solving the one dimensional Bratu problem with efficient fourth order iterative methods. SeMA Journal 71:1, pages 1-14.
Crossref
Manoj Kumar & Neha Yadav. (2015) Numerical Solution of Bratu’s Problem Using Multilayer Perceptron Neural Network Method. National Academy Science Letters 38:5, pages 425-428.
Crossref
Yinghong Xu, Xiangjie Li & Lipu Zhang. (2015) The Particle Swarm Shooting Method for Solving the Bratu's Problem. Journal of Algorithms & Computational Technology 9:3, pages 291-302.
Crossref
W. M. Abd-Elhameed, Y. H. Youssri & E. H. Doha. (2015) 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 9:2, pages 93-102.
Crossref
Randhir Singh, Gnaneshwar Nelakanti & Jitendra Kumar. (2014) 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 85:1, pages 51-61.
Crossref
Xiaomin Wang, Xiaojing Liu, Jizeng Wang & Youhe Zhou. (2015) A wavelet method for bending of circular plate with large deflection. Acta Mechanica Solida Sinica 28:1, pages 83-90.
Crossref
Mustafa Inc, Ali Akgül & Fazhan Geng. (2014) Reproducing Kernel Hilbert Space Method for Solving Bratu’s Problem. Bulletin of the Malaysian Mathematical Sciences Society 38:1, pages 271-287.
Crossref
XiaoJing Liu, YouHe Zhou, Lei Zhang & JiZeng Wang. (2014) Wavelet solutions of Burgers’ equation with high Reynolds numbers. Science China Technological Sciences 57:7, pages 1285-1292.
Crossref
Muhammad Asif Zahoor Raja & Siraj-ul-Islam Ahmad. (2012) Numerical treatment for solving one-dimensional Bratu problem using neural networks. Neural Computing and Applications 24:3-4, pages 549-561.
Crossref
H. Caglar, N. Caglar & M. Ozer. (2014) B-Spline Solution and the Chaotic Dynamics of Troesch's Problem. Acta Physica Polonica A 125:2, pages 554-560.
Crossref
Zaer Abo-Hammour, Omar Abu Arqub, Shaher Momani & Nabil Shawagfeh. (2014) Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm. Discrete Dynamics in Nature and Society 2014, pages 1-15.
Crossref
A. Mohsen. (2014) A simple solution of the Bratu problem. Computers & Mathematics with Applications 67:1, pages 26-33.
Crossref
Changqing Yang & Jianhua Hou. (2013) Chebyshev wavelets method for solving Bratu’s problem. Boundary Value Problems 2013:1.
Crossref
A. Mohsen. (2013) On the integral solution of the one-dimensional Bratu problem. Journal of Computational and Applied Mathematics 251, pages 61-66.
Crossref
E. H. Doha, A. H. Bhrawy, D. Baleanu & R. M. Hafez. (2013) Efficient Jacobi-Gauss collocation method for solving initial value problems of Bratu type. Computational Mathematics and Mathematical Physics 53:9, pages 1292-1302.
Crossref
Xiaojing Liu, Youhe Zhou, Xiaomin Wang & Jizeng Wang. (2013) A wavelet method for solving a class of nonlinear boundary value problems. Communications in Nonlinear Science and Numerical Simulation 18:8, pages 1939-1948.
Crossref
M. A. Hajji & Q. M. Al-Mdallal. (2013) Modified Sinc-Galerkin Method for Nonlinear Boundary Value Problems. Journal of Mathematics 2013, pages 1-10.
Crossref
A. Kazemi Nasab, Z. Pashazadeh Atabakan & A. Kılıçman. (2013) An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method. Mathematical Problems in Engineering 2013, pages 1-10.
Crossref
W. M. Abd-Elhameed, E. H. Doha & Y. H. Youssri. (2013) New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations. Abstract and Applied Analysis 2013, pages 1-9.
Crossref
S. Abbasbandy, M.S. Hashemi & Chein-Shan Liu. (2011) The Lie-group shooting method for solving the Bratu equation. Communications in Nonlinear Science and Numerical Simulation 16:11, pages 4238-4249.
Crossref
R. Jalilian. (2010) Non-polynomial spline method for solving Bratu's problem. Computer Physics Communications 181:11, pages 1868-1872.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.