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Analytical solution for the time-dependent Emden–Fowler type of equations by Adomian decomposition method. (English) Zbl 1073.65105
Summary: The Adomian decomposition method is used to obtain an analytical solution for the time-dependent Emden-Fowler type of equations and a wave-type equation with singular behavior. The advantage of this single global method is employed to present a reliable framework is used to overcome the singularity behavior at the point x=0 for both models. The proposed scheme reveals quite a number of remarkable features that will be helpful for identical problems. The work is supported by analyzing few examples where the convergence of the results is observed.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35K55Nonlinear parabolic equations
65L05Initial value problems for ODE (numerical methods)
65M12Stability and convergence of numerical methods (IVP of PDE)
65L20Stability and convergence of numerical methods for ODE
34A34Nonlinear ODE and systems, general