Year: 1998
Author: Yuanming Wang, Benyu Guo
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 4 : pp. 345–356
Abstract
Nonlinear Jacobi iteration and nonlinear Gauss-Seidel iteration are proposed to solve the famous Numerov finite difference scheme for nonlinear two-points boundary value problem. The concept of supersolutions and subsolutions for nonlinear algebraic systems are introduced. By taking such solutions as initial values, the above two iterations provide monotone sequences, which tend to the solutions of Numerov scheme at geometric convergence rates. The global existence and uniqueness of solution of Numerov scheme are discussed also. The numerical results show the advantages of these two iterations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9165
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 4 : pp. 345–356
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Nonlinear two-points boundary value problem New iterations for Nomerov scheme Monotone approximations.