{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:13:57Z","timestamp":1759191237487},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The present paper is devoted to the development of the theory of monotone\ndifference schemes, approximating the so-called weakly coupled system of linear elliptic\nand quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the\nvector-difference schemes is introduced and the definition of its monotonicity is given.\nThis definition is closely associated with the property of non-negativity of the solution. Under\nthe fulfillment of the positivity condition of the coefficients, two-side estimates of\nthe approximate solution of these vector-difference equations are established and the important\na priori estimate in the uniform norm <jats:italic>C<\/jats:italic> is given.<\/jats:p>","DOI":"10.1515\/cmam-2016-0046","type":"journal-article","created":{"date-parts":[[2017,1,12]],"date-time":"2017-01-12T10:01:00Z","timestamp":1484215260000},"page":"287-298","source":"Crossref","is-referenced-by-count":5,"title":["Monotone Difference Schemes for Weakly Coupled Elliptic and Parabolic Systems"],"prefix":"10.1515","volume":"17","author":[{"given":"Piotr","family":"Matus","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin,Al. Raclawickie 14, 20-950 Lublin, Poland; and Institute of Mathematics, NAS of Belarus, 11 Surganov Str.,20072 Minsk, Belarus"}]},{"given":"Francisco","family":"Gaspar","sequence":"additional","affiliation":[{"name":"CWI, Centrum Wiskunde and Informatica, Amsterdam, Netherlands"}]},{"given":"Le Minh","family":"Hieu","sequence":"additional","affiliation":[{"name":"Belarusian State University, 4 Nezavisimosti avenue, 220030 Minsk, Belarus;and University of Economics, The University of Danang, 71 Ngu Hanh Son Str., 590000 Danang, Vietnam"}]},{"given":"Vo Thi Kim","family":"Tuyen","sequence":"additional","affiliation":[{"name":"Belarusian State University, 4 Nezavisimosti avenue, 220030 Minsk, Belarus"}]}],"member":"374","published-online":{"date-parts":[[2017,1,12]]},"reference":[{"key":"2023033114222309557_j_cmam-2016-0046_ref_001_w2aab3b7e2887b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"Farago I. and Horvath R.,\nDiscrete maximum principle and adequate discretizations of linear parabolic problems,\nSIAM J. 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Nauk Belarusi 44 (2000), no. 4, 21\u201325."},{"key":"2023033114222309557_j_cmam-2016-0046_ref_005_w2aab3b7e2887b1b6b1ab2ab5Aa","unstructured":"Manaa S. A.,\nSome numerical methods for schnackenberg model,\nIntern. J. Eng. Inventions 2 (2013), no. 2, 71\u201378."},{"key":"2023033114222309557_j_cmam-2016-0046_ref_006_w2aab3b7e2887b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"Matus P. P.,\nMonotone schemes of a higher order of accuracy for differential problems with boundary conditions of the second and third kind,\nComput. Methods Appl. Math. 2 (2002), no. 4, 378\u2013391.","DOI":"10.2478\/cmam-2002-0021"},{"key":"2023033114222309557_j_cmam-2016-0046_ref_007_w2aab3b7e2887b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"Matus P. P.,\nThe maximum principle and some of its applications,\nComput. Methods Appl. Math. 2 (2002), no. 1, 50\u201391.","DOI":"10.2478\/cmam-2002-0004"},{"key":"2023033114222309557_j_cmam-2016-0046_ref_008_w2aab3b7e2887b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"Matus P. P.,\nOn convergence of difference schemes for ibvp for quasilinear parabolic equation with generalized solutions,\nComput. Methods Appl. Math. 14 (2014), no. 3, 361\u2013371.","DOI":"10.1515\/cmam-2014-0008"},{"key":"2023033114222309557_j_cmam-2016-0046_ref_009_w2aab3b7e2887b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"Matus P. P., Hieu L. M. and Volkov L. G.,\nAnalysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations,\nJ. Comput. Appl. Math. 310 (2017), no. C, 186\u2013199.","DOI":"10.1016\/j.cam.2016.04.006"},{"key":"2023033114222309557_j_cmam-2016-0046_ref_010_w2aab3b7e2887b1b6b1ab2ac10Aa","unstructured":"Matus P. P., Tuyen V. T. K. and Gaspar F. 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