Continuation Methods for Nonlinear Eigenvalue Problems via a Sinc-Galerkin Scheme
作者： Jack D. Dockery , Nancy J. Lybeck
DOI: 10.1007/978-1-4612-0321-6_11
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摘要: In this paper we will be looking at semilinear boundary value problems of the form $$ \begin{gathered} \mathcal{L}u(x)\bar = u^{''} (x) + cu(x) f(x,u(x),\lambda ),a < x b \hfill \\ u(a) u(b) 0, \end{gathered} $$ (1.1) where c is a fixed constant and A parameter. Here, need not finite. This type problem often arises as equilibrium for scalar evolution equation. The purpose to illustrate use Sinc-Galerkin method one-parameter such (1.1).
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sci-hub.st 参考文章(9)
Gerald Ryder, Boundary value problems for a class of nonlinear differential equations Pacific Journal of Mathematics. ,vol. 22, pp. 477- 503 ,(1967) , 10.2140/PJM.1967.22.477
R. Glowinski, H. B. Keller, L. Reinhart, Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems SIAM Journal on Scientific and Statistical Computing. ,vol. 6, pp. 793- 832 ,(1985) , 10.1137/0906055
C. Jones, T. Küpper, On the Infinitely Many Solutions of a Semilinear Elliptic Equation SIAM Journal on Mathematical Analysis. ,vol. 17, pp. 803- 835 ,(1986) , 10.1137/0517059
T. M. Hagstrom, H. B. Keller, Asymptotic boundary conditions and numerical methods for nonlinear elliptic problems on unbounded domains Mathematics of Computation. ,vol. 48, pp. 449- 470 ,(1987) , 10.1090/S0025-5718-1987-0878684-5
Frank Stenger, A “sinc-Galerkin” method of solution of boundary value problems Mathematics of Computation. ,vol. 33, pp. 85- 109 ,(1979) , 10.1090/S0025-5718-1979-0514812-4
Jean Chauvette, Frank Stenger, The approximate solution of the nonlinear equation Δu = u − u3 Journal of Mathematical Analysis and Applications. ,vol. 51, pp. 229- 242 ,(1975) , 10.1016/0022-247X(75)90155-9
Frank Stenger, Numerical Methods Based on Whittaker Cardinal, or Sinc Functions Siam Review. ,vol. 23, pp. 165- 224 ,(1981) , 10.1137/1023037
Eugene L. Allgower, Kurt Georg, Numerical Continuation Methods: An Introduction ,(2011)
Eugene L. Allgower, Kurt Georg, Numerical Continuation Methods Springer Series in Computational Mathematics. ,(1990) , 10.1007/978-3-642-61257-2