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Zbl 1191.65105
Adiyaman, Meltem Evrenosoglu; Somali, Sennur
Taylor's decomposition on two points for one-dimensional Bratu problem. (English)
[J] Numer. Methods Partial Differ. Equations 26, No. 2, 412-425 (2010). ISSN 0749-159X; ISSN 1098-2426/e

The authors present a Taylor's decomposition method on two points to approximate the one-dimensional nonlinear Bratu problem. They first derive an equivalent first order differential equation system. A Taylor's decomposition method on two points is applied to approximate this first order differential equation system. The computation of the eigenvalues of the problem is given. The application and error analysis of the method for the nonlinear initial value problem corresponding to the Bratu problem are discussed. Numerical tests justifying the efficiency of the numerical method are presented.
[Abdallah Bradji (Tebessa)]

MSC 2000:: *65L15 Eigenvalue problems for ODE (numerical methods)
65L10 Boundary value problems for ODE (numerical methods)
34L15 Estimation of eigenvalues for OD operators
34L30 Nonlinear ordinary differential operators
65L70 Error bounds (numerical methods for ODE)

Keywords: Taylor's decomposition method on two points; numerical examples; nonlinear eigenvalue problems; one-dimensional nonlinear Bratu problem; nonlinear initial value problem

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