Čiegis, R.; Tumanova, N. Numerical solution of parabolic problems with nonlocal boundary conditions. (English) Zbl 1211.65109 Numer. Funct. Anal. Optim. 31, No. 12, 1318-1329 (2010). The authors use the implicit Euler finite difference scheme to solve a parabolic equation with nonlocal integral boundary condition. A stability analysis in the maximum norm and a numerical example are also presented. Reviewer: Damian Słota (Gliwice) Cited in 16 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:implicit Euler finite difference scheme; nonlocal boundary condition; parabolic problem; convergence; regularization; implicit Euler finite difference scheme; stability; numerical example Software:Parsol PDFBibTeX XMLCite \textit{R. Čiegis} and \textit{N. Tumanova}, Numer. Funct. Anal. Optim. 31, No. 12, 1318--1329 (2010; Zbl 1211.65109) Full Text: DOI References: [1] Bouziani A., Acad. Roy. Belg. Bull. Cl. Sci. 10 pp 61– (1999) [2] DOI: 10.1016/0020-7225(90)90086-X · Zbl 0721.65046 · doi:10.1016/0020-7225(90)90086-X [3] DOI: 10.1016/0020-7225(93)90010-R · Zbl 0773.65069 · doi:10.1016/0020-7225(93)90010-R [4] Čiegis R., Math. Model. Anal. 6 pp 178– (2001) [5] DOI: 10.1023/A:1021167932414 · Zbl 1030.65092 · doi:10.1023/A:1021167932414 [6] Čiegis R., Informatica 17 pp 309– (2006) [7] Day W.A., Quart. Appl. Math. 41 pp 468– (1983) · Zbl 0514.35038 · doi:10.1090/qam/693879 [8] Day W.A., Quart. Appl. Math. 50 pp 523– (1992) · Zbl 0794.35069 · doi:10.1090/qam/1178432 [9] DOI: 10.1016/j.apnum.2004.02.002 · Zbl 1063.65079 · doi:10.1016/j.apnum.2004.02.002 [10] DOI: 10.1007/BF01931285 · Zbl 0738.65074 · doi:10.1007/BF01931285 [11] DOI: 10.1007/BF02127706 · Zbl 0868.65068 · doi:10.1007/BF02127706 [12] Friedman A., Quart. Appl. Math. 44 pp 401– (1986) · Zbl 0631.35041 · doi:10.1090/qam/860893 [13] Goolin A.V., Comp. Meth. Appl. Math. 1 pp 62– (2001) [14] Ionkin N.I., Differential Equations 15 pp 911– (1980) [15] DOI: 10.1016/j.apnum.2008.07.001 · Zbl 1167.65422 · doi:10.1016/j.apnum.2008.07.001 [16] DOI: 10.1016/j.apnum.2009.05.007 · Zbl 1167.65423 · doi:10.1016/j.apnum.2009.05.007 [17] Samarskii A.A., Differential Equations 16 pp 1221– (1980) [18] DOI: 10.1016/S0377-0427(96)00097-0 · Zbl 0873.65129 · doi:10.1016/S0377-0427(96)00097-0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.