Caglar, Hikmet; Caglar, Nazan; Özer, Mehmet; Valarıstos, Antonios; Anagnostopoulos, Antonios N. B-spline method for solving Bratu’s problem. (English) Zbl 1197.65090 Int. J. Comput. Math. 87, No. 8, 1885-1891 (2010). Summary: We propose a B-spline method for solving the one-dimensional Bratu’s problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur. Cited in 59 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations Keywords:Bratu’s problem; B-spline method; nonlinear boundary value problem; Laplace method; decomposition method; numerical examples; bifurcation PDFBibTeX XMLCite \textit{H. Caglar} et al., Int. J. Comput. Math. 87, No. 8, 1885--1891 (2010; Zbl 1197.65090) Full Text: DOI References: [1] Aregbesola Y. A.S., Electron. J. South. Afr. Math. Sci. 3 pp 1– (2003) [2] DOI: 10.1007/BF01061392 · Zbl 0649.65057 · doi:10.1007/BF01061392 [3] DOI: 10.1016/S0096-3003(02)00345-4 · Zbl 1025.65042 · doi:10.1016/S0096-3003(02)00345-4 [4] DOI: 10.1002/num.10055 · Zbl 1079.76048 · doi:10.1002/num.10055 [5] DOI: 10.1002/num.10093 · Zbl 1048.65102 · doi:10.1002/num.10093 [6] Caglar H., Chaos Solitons Fractals (2007) [7] de Boor C., A Practical Guide to Splines (1978) · Zbl 0406.41003 [8] DOI: 10.1006/jcph.2000.6452 · Zbl 0959.65091 · doi:10.1006/jcph.2000.6452 [9] Fletcher R., Practical Methods of Optimization (1987) · Zbl 0905.65002 [10] Frank-Kamenetski D. A., Diffusion and Heat Exchange in Chemical Kinetics (1955) [11] Hassan I. H.A.H., Int. J. Contemp. Math. Sci. 2 pp 1493– (2007) [12] DOI: 10.1142/S0217979206033796 · Zbl 1102.34039 · doi:10.1142/S0217979206033796 [13] DOI: 10.1006/jdeq.2001.4151 · Zbl 1015.34013 · doi:10.1006/jdeq.2001.4151 [14] DOI: 10.1016/S0096-3003(02)00656-2 · Zbl 1032.65084 · doi:10.1016/S0096-3003(02)00656-2 [15] DOI: 10.1016/j.amc.2004.09.066 · Zbl 1151.35354 · doi:10.1016/j.amc.2004.09.066 [16] DOI: 10.1111/j.1467-9590.2007.00387.x · doi:10.1111/j.1467-9590.2007.00387.x [17] DOI: 10.1016/S0096-3003(97)81660-8 · Zbl 0908.65094 · doi:10.1016/S0096-3003(97)81660-8 [18] Mounim A. S., Numer. Methods Partial Differen. Eqns. [19] DOI: 10.1016/j.amc.2005.10.021 · Zbl 1093.65108 · doi:10.1016/j.amc.2005.10.021 [20] DOI: 10.1016/j.amc.2004.06.059 · Zbl 1073.65068 · doi:10.1016/j.amc.2004.06.059 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.