A new method for solving singular initial value problems in the second-order ordinary differential equations. (English) Zbl 1030.34004

Summary: Singular initial value problems, linear and nonlinear, homogeneous and nonhomogeneous, are investigated by using the Adomian decomposition method. The solutions are constructed in the form of a convergent series. A new general formula is established. The approach is illustrated with few examples.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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