In this paper, we solve coupled Lane-Emden equations arising in catalytic diffusion reaction by reproducing kernel Hilbert space method. First, we construct a reproducing kernel Hilbert space satisfying boundary value conditions and provide an iterative method to obtain the approximate solution. Then we present four numerical example to show our method is accurate and reliable.Our method overcomes the singular behavior at x = 0. Finally we compare our method with ADM and Modified ADM on the maximal error remainder, which demonstrates an approximate exponential rate of convergence.
This paper deals with the stability of the orbits for time-dependent nearly integrable Hamiltonian systems. Under the classical non-degeneracy in KAM theory we prove that the considered system possesses quasi-effective stability. Our result generalized the works in [F. Z. Cong, J. L. Hong, H. T. Li, Dyn. Syst. Ser. B, 21 (2016), 67-80] to time-dependent system and gave a connection between KAM theorem and effective stability.
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