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Zh. Vychisl. Mat. Mat. Fiz.:

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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 9, Page 1480 (Mi zvmmf9915)  

This article is cited in 5 scientific papers (total in 5 papers)

Efficient Jacobi–Gauss collocation method for solving initial value problems of Bratu-type

E. H. Dohaa, A. H. Bhrawybc, D. Baleanudce, R. H. Hafezf

a Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
b Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
c King Abdulaziz University, Jeddah
d epartment of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey
e Institute of Space Sciences, Magurele-Bucharest, Romania
f Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, Egypt

Abstract: In this paper, we propose the shifted Jacobi–Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials $J_n^{(\alpha,\beta)}(x)$ with $\alpha, \beta \in(-1,\infty)$, $x\in[0,1]$ and $n$ the polynomial degree. The shifted Jacobi–Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.

Key words: Bratu-type equations, second-order initial value problems, collocation method, Jacobi–Gauss quadrature, shifted Jacobi polynomials.


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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:9, 1292–1302

Bibliographic databases:

UDC: 519.62
Received: 11.02.2013

Citation: E. H. Doha, A. H. Bhrawy, D. Baleanu, R. H. Hafez, “Efficient Jacobi–Gauss collocation method for solving initial value problems of Bratu-type”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1480; Comput. Math. Math. Phys., 53:9 (2013), 1292–1302

Citation in format AMSBIB
\by E.~H.~Doha, A.~H.~Bhrawy, D.~Baleanu, R.~H.~Hafez
\paper Efficient Jacobi--Gauss collocation method for solving initial value problems of Bratu-type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
\issue 9
\pages 1480
\jour Comput. Math. Math. Phys.
\yr 2013
\vol 53
\issue 9
\pages 1292--1302

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    This publication is cited in the following articles:
    1. Doha E.H., Baleanu D., Bhrawi A.H., Hafez R.M., “A Jacobi Collocation Method for Troesch's Problem in Plasma Physics”, Proc. Rom. Acad. Ser. A-Math. Phys., 15:2 (2014), 130–138  mathscinet  isi
    2. Doha E.H., Bhrawy A.H., Baleanu D., Abdelkawy M.A., “Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations”, Rom. J. Phys., 59:3-4 (2014), 247–264  isi
    3. S. Deniz, N. Bildik, “Optimal perturbation iteration method for Bratu-type problems”, J. King Saud Univ. Sci., 30:1 (2018), 91–99  crossref  isi  scopus
    4. E. Keshavarz, Y. Ordokhani, M. Razzaghi, “The Taylor wavelets method for solving the initial and boundary value problems of Bratu-type equations”, Appl. Numer. Math., 128 (2018), 205–216  crossref  mathscinet  zmath  isi  scopus
    5. Tomar S., Pandey R.K., “An Efficient Iterative Method For Solving Bratu-Type Equations”, J. Comput. Appl. Math., 357 (2019), 71–84  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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