caa a22 4500 605496854 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10543-014-0529-6 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0529-6 Boglaev Igor Institute of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, New Zealand aut Monotone iterative ADI method for semilinear parabolic problems [Elektronische Daten] [Igor Boglaev] The paper deals with numerical solving semilinear parabolic problems based on a nonlinear alternating direction implicit (ADI) scheme. The convergence of the nonlinear ADI scheme to the continuous solution is proved. The existence and uniqueness of a solution of the nonlinear ADI scheme are established. A monotone iterative ADI method is constructed. An analysis of convergence of the monotone iterative ADI method to the solution of the nonlinear ADI scheme on the whole time interval is given. Numerical experiments are presented. Springer Science+Business Media Dordrecht, 2014 Semilinear parabolic problem nationallicence Nonlinear ADI scheme nationallicence Upper and lower solutions nationallicence Monotone iterations nationallicence Monotone iterative ADI method nationallicence BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 647-676 0006-3835 55:3<647 2015 55 10543 https://doi.org/10.1007/s10543-014-0529-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0529-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Boglaev Igor Institute of Fundamental Sciences, Massey University, Private Bag 11-222, Palmerston North, New Zealand aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/3(2015-09-01), 647-676 0006-3835 55:3<647 2015 55 10543