An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions

[1]  Saullo G.P. Castro,et al.  Nonlinear bifurcation analysis of stiffener profiles via deflation techniques , 2020, Thin-Walled Structures.

[2]  Yingwei Wang,et al.  Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions , 2018, SIAM J. Sci. Comput..

[3]  Ziqing Xie,et al.  An augmented singular transform and its partial Newton method for finding new solutions , 2015, J. Comput. Appl. Math..

[4]  Simon W. Funke,et al.  Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations , 2014, SIAM J. Sci. Comput..

[5]  Wenrui Hao,et al.  A bootstrapping approach for computing multiple solutions of differential equations , 2014, J. Comput. Appl. Math..

[6]  Jintao Zhang,et al.  Eigenfunction Expansion Method for Multiple Solutions of Semilinear Elliptic Equations with Polynomial Nonlinearity , 2013, SIAM J. Numer. Anal..

[7]  Andrew R. Conn,et al.  On the local convergence of a derivative-free algorithm for least-squares minimization , 2012, Comput. Optim. Appl..

[8]  E. Tadmor A review of numerical methods for nonlinear partial differential equations , 2012 .

[9]  Jie Shen,et al.  Spectral Methods: Algorithms, Analysis and Applications , 2011 .

[10]  Ya-Xiang Yuan,et al.  Optimization Theory and Methods: Nonlinear Programming , 2010 .

[11]  S. Liao,et al.  Homotopy based solutions of the Navier–Stokes equations for a porous channel with orthogonally moving walls , 2010 .

[12]  Ben-yu Guo,et al.  Composite Laguerre-Legendre spectral method for exterior problems , 2010, Adv. Comput. Math..

[13]  Jianxin Zhou,et al.  A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems , 2010, Math. Comput..

[14]  Christopher C. Tisdell,et al.  On the solvability of two-point, second-order boundary value problems , 2007, Appl. Math. Lett..

[15]  Xudong Yao,et al.  Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases , 2007, SIAM J. Sci. Comput..

[16]  Yun Xu,et al.  AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES * * This research was supported by t , 2006 .

[17]  Yun Xu,et al.  An improved search-extension method for computing multiple solutions of semilinear PDEs , 2005 .

[18]  Nicholas I. M. Gould,et al.  A Filter-Trust-Region Method for Unconstrained Optimization , 2005, SIAM J. Optim..

[19]  D. J. Bates,et al.  Solution of Polynomial Systems Derived from Differential Equations , 2005, Computing.

[20]  Xudong Yao,et al.  A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE , 2005, SIAM J. Sci. Comput..

[21]  Jianxin Zhou,et al.  Instability analysis of saddle points by a local minimax method , 2004, Math. Comput..

[22]  W. E,et al.  Minimum action method for the study of rare events , 2004 .

[23]  J. Majdalani,et al.  Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls , 2003 .

[24]  U. Frisch,et al.  A reconstruction of the initial conditions of the Universe by optimal mass transportation , 2001, Nature.

[25]  Yongxin Li,et al.  A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs , 2001, SIAM J. Sci. Comput..

[26]  Michael Plum,et al.  Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof , 2000 .

[27]  T. Ouyang,et al.  EXACT MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR PROBLEMS , 1998 .

[28]  Goong Chen,et al.  A high-linking algorithm for sign-changing solutions of semilinear elliptic equations , 1999 .

[29]  Y. Choi,et al.  A mountain pass method for the numerical solution of semilinear elliptic problems , 1993 .

[30]  P. Lions On the Existence of Positive Solutions of Semilinear Elliptic Equations , 1982 .

[31]  A. A. Grau Rounding Errors in Algebraic Processes (J. H. Wilkinson) , 1966 .

[32]  H. Davis Introduction to Nonlinear Differential and Integral Equations , 1964 .

[33]  E. Allgower,et al.  Application of numerical continuation to compute all solutions of semilinear elliptic equations , 2009 .

[34]  Xudong Yao,et al.  Numerical Methods for Computing Nonlinear Eigenpairs: Part II. Non-Iso-Homogeneous Cases , 2008, SIAM J. Sci. Comput..

[35]  Ziqing Xie,et al.  Structure of multiple solutions for nonlinear differential equations , 2004 .

[36]  Ziqing Xie,et al.  Search extension method for multiple solutions of a nonlinear problem , 2004 .

[37]  Zhi-Qiang Wang On a superlinear elliptic equation , 1991 .

[38]  W. A. Robinson The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls , 1976 .

[39]  W. B. Gearhart,et al.  Deflation techniques for the calculation of further solutions of a nonlinear system , 1971 .

[40]  Xiaomei Yang Rounding Errors in Algebraic Processes , 1964, Nature.