%0 Journal Article %T The quadratic convergence of approximate solutions for singular difference systems with "maxima" %A Wang, Peiguang %A Liu, Xiang %J Journal of Mathematics and Computer Science %D 2016 %V 16 %N 2 %@ ISSN 2008-949X %F Wang2016 %X 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. %9 journal article %R 10.22436/jmcs.016.02.11 %U http://dx.doi.org/10.22436/jmcs.016.02.11 %P 227-238 %0 Journal Article %T Singular difference equations: an overview %A P. K. Anh %A N. H. Du %A L. C. Loi %J Vietnam J. Math. %D 2007 %V 35 %F Anh2007 %0 Journal Article %T Stability of a class of singular difference equations %A P. K. Anh %A D. S. Hoang %J Int. J. Difference Equ. %D 2006 %V 1 %F Anh2006 %0 Journal Article %T On the solvability of initial-value problems for nonlinear implicit difference equations %A P. K. Anh %A H. T. N. Yen %J Adv. Difference Equ %D 2004 %V 24 %F Anh2004 %0 Journal Article %T First order difference equations with maxima and nonlinear functional boundary value conditions %A F. M. Atici %A A. Cabada %A J. B. Ferreiro %J J. Difference Equ. Appl. %D 2006 %V 12 %F Atici2006 %0 Book %T Differential equations with maxima %A D. D. Bainov %A S. G. Hristova %D 2011 %I CRC Press %C London and New York %F Bainov2011 %0 Book %T Quasilinearization and Nonlinear Boundary Value Problems %A R. E. Bellman %A R. E. Kalaba %D 1965 %I American Elsevier Publishing Co., Inc. %C New York %F Bellman1965 %0 Book %T Singular systems of differential equations %A S. L. Campbell %D 1980 %I Pitman Advanced Publishing Program (I) %C London %F Campbell1980 %0 Book %T Singular systems of differential equations %A S. L. Campbell %D 1982 %I Pitman Advanced Publishing Program (II) %C London %F Campbell1982 %0 Journal Article %T On the asymptotic behavior and periodic nature of a difference equation with maximum %A A. Gelişken %A C. Çinar %A A. S. Kurbanli %J Comput. Math. Appl. %D 2010 %V 59 %F Gelişken2010 %0 Journal Article %T Quasilinearization of the initial value problem for difference equations with ''maxima'' %A S. Hristova %A A. Golev %A K. Stefanova %J J. Appl. Math. %D 2012 %V 2012 %F Hristova2012 %0 Book %T Generalized quasilinearization for nonlinear problems %A V. Lakshmikantham %A A. S. Vatsala %D 1998 %I Kluwer Academic Publishers %C Dordrecht %F Lakshmikantham1998 %0 Journal Article %T Global stability of a difference equation with maximum %A S. Stević %J Appl. Math. Comput. %D 2009 %V 210 %F Stević2009 %0 Journal Article %T Rapid convergence of solution of nonlinear singular difference system %A P. G. Wang %A T. T. Kong %J J. Nat. Sci. Heilongjiang Univ. %D 2010 %V 27 %F Wang2010 %0 Journal Article %T Monotone iterative technique for initial-value problems of nonlinear singular discrete systems %A P. Wang %A J. Zhang %J J. Comput. Appl. Math. %D 2008 %V 221 %F Wang2008 %0 Journal Article %T On a difference equation wtih maximum %A X. Yang %A X. Liao %A C. Li %J Appl. Math. Comput. %D 2006 %V 181 %F Yang2006 %0 Journal Article %T Optimal model reduction of discrete-time descriptor systems %A L. Zhang %A J. Lam %A Q. Zhang %J Internat. J. Systems Sci. %D 2000 %V 132 %F Zhang2000