TY - JOUR AU - Wang, Peiguang AU - Liu, Xiang PY - 2016 TI - The quadratic convergence of approximate solutions for singular difference systems with "maxima" JO - Journal of Mathematics and Computer Science SP - 227-238 VL - 16 IS - 2 AB - This paper investigates the initial value problem of singular difference systems with maxima. An algorithm based on quasilinearization is suggested to solve the initial value problem for the nonlinear singular difference system with maxima, and the quadratic convergences of the sequence of successive approximations are obtained. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.016.02.11 DO - 10.22436/jmcs.016.02.11 ID - Wang2016 ER - TY - JOUR TI - Singular difference equations: an overview AU - P. K. Anh AU - N. H. Du AU - L. C. Loi JO - Vietnam J. Math. PY - 2007 DA - 2007// VL - 35 ID - Anh2007 ER - TY - JOUR TI - Stability of a class of singular difference equations AU - P. K. Anh AU - D. S. Hoang JO - Int. J. Difference Equ. PY - 2006 DA - 2006// VL - 1 ID - Anh2006 ER - TY - JOUR TI - On the solvability of initial-value problems for nonlinear implicit difference equations AU - P. K. Anh AU - H. T. N. Yen JO - Adv. Difference Equ PY - 2004 DA - 2004// VL - 24 ID - Anh2004 ER - TY - JOUR TI - First order difference equations with maxima and nonlinear functional boundary value conditions AU - F. M. Atici AU - A. Cabada AU - J. B. Ferreiro JO - J. Difference Equ. Appl. PY - 2006 DA - 2006// VL - 12 ID - Atici2006 ER - TY - BOOK TI - Differential equations with maxima AU - D. D. Bainov AU - S. G. Hristova PB - CRC Press PY - 2011 DA - 2011// CY - London and New York ID - Bainov2011 ER - TY - BOOK TI - Quasilinearization and Nonlinear Boundary Value Problems AU - R. E. Bellman AU - R. E. Kalaba PB - American Elsevier Publishing Co., Inc. PY - 1965 DA - 1965// CY - New York ID - Bellman1965 ER - TY - BOOK TI - Singular systems of differential equations AU - S. L. Campbell PB - Pitman Advanced Publishing Program (I) PY - 1980 DA - 1980// CY - London ID - Campbell1980 ER - TY - BOOK TI - Singular systems of differential equations AU - S. L. Campbell PB - Pitman Advanced Publishing Program (II) PY - 1982 DA - 1982// CY - London ID - Campbell1982 ER - TY - JOUR TI - On the asymptotic behavior and periodic nature of a difference equation with maximum AU - A. Gelişken AU - C. Çinar AU - A. S. Kurbanli JO - Comput. Math. Appl. PY - 2010 DA - 2010// VL - 59 ID - Gelişken2010 ER - TY - JOUR TI - Quasilinearization of the initial value problem for difference equations with ''maxima'' AU - S. Hristova AU - A. Golev AU - K. Stefanova JO - J. Appl. Math. PY - 2012 DA - 2012 // VL - 2012 ID - Hristova2012 ER - TY - BOOK TI - Generalized quasilinearization for nonlinear problems AU - V. Lakshmikantham AU - A. S. Vatsala PB - Kluwer Academic Publishers PY - 1998 DA - 1998// CY - Dordrecht ID - Lakshmikantham1998 ER - TY - JOUR TI - Global stability of a difference equation with maximum AU - S. Stević JO - Appl. Math. Comput. PY - 2009 DA - 2009// VL - 210 ID - Stević2009 ER - TY - JOUR TI - Rapid convergence of solution of nonlinear singular difference system AU - P. G. Wang AU - T. T. Kong JO - J. Nat. Sci. Heilongjiang Univ. PY - 2010 DA - 2010// VL - 27 ID - Wang2010 ER - TY - JOUR TI - Monotone iterative technique for initial-value problems of nonlinear singular discrete systems AU - P. Wang AU - J. Zhang JO - J. Comput. Appl. Math. PY - 2008 DA - 2008// VL - 221 ID - Wang2008 ER - TY - JOUR TI - On a difference equation wtih maximum AU - X. Yang AU - X. Liao AU - C. Li JO - Appl. Math. Comput. PY - 2006 DA - 2006// VL - 181 ID - Yang2006 ER - TY - JOUR TI - Optimal model reduction of discrete-time descriptor systems AU - L. Zhang AU - J. Lam AU - Q. Zhang JO - Internat. J. Systems Sci. PY - 2000 DA - 2000// VL - 132 ID - Zhang2000 ER -