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Zbl 1162.65399
Yang, Pei; Chen, Yong; Li, Zhi-Bin
ADM-Padé technique for the nonlinear lattice equations. (English)
[J] Appl. Math. Comput. 210, No. 2, 362-375 (2009). ISSN 0096-3003

Summary: ADM-Padé technique is a combination of Adomian decomposition method (ADM) and Padé approximants. We solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence rate than using ADM alone. Bell-shaped solitary solution of Belov-Chaltikian (BC) lattice and kink-shaped solitary solution of the nonlinear self-dual network equations (SDNEs) are presented. Comparisons are made between approximate solutions and exact solutions to illustrate the validity and the great potential of the technique.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)

Keywords: Adomian decomposition method; Padé approximants; Belov-Chaltikian lattice; the nonlinear self-dual network equations; solitary solution

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Zentralblatt MATH Berlin [Germany]