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Numerical methods and asymptotic error expansions for the Emden-Fowler equations. (English) Zbl 0854.65067
The author solves the boundary value problem \[ y''(x) + cx^p[y(x)]^q = 0,\quad x \in (0,1), \quad y(0) = 1,\quad y(1) = 0. \] The approximate solution is obtained in two stages. In the first stage, the Picard method is applied for linearization. In the second stage, for finding in each iteration an approximate solution of the appropriate linear boundary value problem the method of grids is applied. On the basis of asymptotic expansions for the discretization error, the author uses the E-algorithm of Brezinski to accelerate the convergence of the numerical solutions obtained by the finite difference method, for the three cases \(p = -{1\over 2}\), \(p = -1\), \(p = -{5\over 4}\). In the end some numerical results are presented.
Reviewer: V.Makarov (Kiev)

MSC:
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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