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Taylor’s decomposition on two points for one-dimensional Bratu problem. (English) Zbl 1191.65105
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.
MSC:
65L15Eigenvalue problems for ODE (numerical methods)
65L10Boundary value problems for ODE (numerical methods)
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
34L30Nonlinear ordinary differential operators
65L70Error bounds (numerical methods for ODE)