An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions
暂无分享,去创建一个
[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.