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Applying differential transformation method to the one-dimensional planar Bratu problem. (English) Zbl 1152.34008

The authors consider the one-dimensional Bratu problem \[ u''+\lambda e^u= 0,\quad u(0)= 0,\quad u(1)= 0. \] A numerical algorithm is described for finding the solution with the help of differential transformation. Numerical examples are given for \(\lambda= 1\) and \(\lambda= 2\).

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
74S30 Other numerical methods in solid mechanics (MSC2010)
65L10 Numerical solution of boundary value problems involving ordinary differential equations
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