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Volume 16, Issue 4
On Numerov Scheme for Nonlinear Two-Points Boundary Value Problem

Yuanming Wang & Benyu Guo

J. Comp. Math., 16 (1998), pp. 345-356.

Published online: 1998-08

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  • 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.

  • Keywords

Nonlinear two-points boundary value problem, New iterations for Nomerov scheme, Monotone approximations.

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COPYRIGHT: © Global Science Press

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@Article{JCM-16-345, author = {Wang , Yuanming and Guo , Benyu}, title = {On Numerov Scheme for Nonlinear Two-Points Boundary Value Problem}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9165.html} }
TY - JOUR T1 - On Numerov Scheme for Nonlinear Two-Points Boundary Value Problem AU - Wang , Yuanming AU - Guo , Benyu JO - Journal of Computational Mathematics VL - 4 SP - 345 EP - 356 PY - 1998 DA - 1998/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9165.html KW - Nonlinear two-points boundary value problem, New iterations for Nomerov scheme, Monotone approximations. AB -

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.

Wang , Yuanming and Guo , Benyu. (1998). On Numerov Scheme for Nonlinear Two-Points Boundary Value Problem. Journal of Computational Mathematics. 16 (4). 345-356. doi:
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