Geodesic
Self-avoiding walks on lattice strips
Serdica Mathematical Journal, Tome 43 (2017) no. 2, pp. 187-210.

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The main purpose of this paper is to study the convergence of numerical solutions to a class of neutral stochastic delay differential equations (NSDDEs) in Itô sense. The basic idea is to reformulate the original problem eliminating the dependence on the differentiation of the solution in the past values, which leads to a stochastic differential algebraic system. It is shown that the Semi-implicit Euler (SIE) method with two parameters θ and λ is mean-square convergent with order p =1/2 for Lipschitz continuous coefficients of underlying NSDDEs. A nonlinear numerical example illustrates the theoretical results.
Keywords: self-avoiding walks, connective constant, honeycomb lattice, asymptotic behavior, 05A15, 05C38, 05C81, 60G50, 82B41 
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Dangovski, R.; Lalov, C. Self-avoiding walks on lattice strips. Serdica Mathematical Journal, Tome 43 (2017) no. 2, pp. 187-210. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_2_a6/