Periodically generated iterative methods for solving elliptic equations

1995 ◽  
Vol 19 (3) ◽  
pp. 375-387 ◽  
Author(s):  
David M. Young ◽  
Shengyou Xiao ◽  
Karen R. Baker
Keyword(s):  
Iterative Methods ◽  
Elliptic Equations

On iterative methods for some elliptic equations with nonlocal conditions

2014 ◽  
Vol 19 (3) ◽  
pp. 517-535 ◽  
Author(s):  
Olga Štikonienė ◽  
◽  
Mifodijus Sapagovas ◽  
Regimantas Čiupaila ◽  
◽  
...  
Keyword(s):  
Iterative Methods ◽  
Elliptic Equations ◽  
Nonlocal Conditions

scholarly journals Numerical solution of nonlinear elliptic systems by block monotone iterations

2019 ◽  
Vol 60 ◽  
pp. C79-C94
Author(s):  
Mohamed Saleh Mehdi Al-Sultani ◽  
Igor Boglaev
Keyword(s):  
Iterative Methods ◽  
Elliptic Equations ◽  
Numerical Solutions ◽  
Upper And Lower Solutions ◽  
Elliptic Systems ◽  
Nonlinear Elliptic Equations ◽  
Difference Schemes ◽  
Uniqueness Of Solutions ◽  
Monotone Iterative ◽  
Nonlinear Elliptic

We present numerical methods for solving a coupled system of nonlinear elliptic problems, where reaction functions are quasimonotone nondecreasing. We utilize block monotone iterative methods based on the Jacobi and Gauss--Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of solutions are discussed. Numerical experiments are presented. References Boglaev, I., Monotone iterates for solving systems of semilinear elliptic equations and applications, ANZIAM J, Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, 49(2008), C591C608. doi:10.21914/anziamj.v49i0.311 Pao, C. V., Nonlinear parabolic and elliptic equations, Springer-Verlag (1992). doi:10.1007/978-1-4615-3034-3 Pao, C. V., Block monotone iterative methods for numerical solutions of nonlinear elliptic equations, Numer. Math., 72(1995), 239262. doi:10.1007/s002110050168 Samarskii, A., The theory of difference schemes, CRC Press (2001). https://www.crcpress.com/The-Theory-of-Difference-Schemes/Samarskii/p/book/9780824704681 Varga, R. S., Matrix iterative analysis, Springer-Verlag (2000). doi:10.1007/978-3-642-05156-2

Sign in / Sign up

Export Citation Format

Share Document