Resumen: The present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is introduced and the definition of its monotonicity is given. This definition is closely associated with the property of non-negativity of the solution. Under the fulfillment of the positivity condition of the coefficients, two-side estimates of the approximate solution of these vector-difference equations are established and the important a priori estimate in the uniform norm C is given. Idioma: Inglés DOI: 10.1515/cmam-2016-0046 Año: 2017 Publicado en: Computational Methods in Applied Mathematics 17, 2 (2017), 287-298 ISSN: 1609-4840 Factor impacto JCR: 0.658 (2017) Categ. JCR: MATHEMATICS, APPLIED rank: 192 / 252 = 0.762 (2017) - Q4 - T3 Factor impacto SCIMAGO: 1.291 - Applied Mathematics (Q1) - Numerical Analysis (Q1) - Computational Mathematics (Q1)