Abstract
Abstract 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.
Highlights
Computational methods satisfying the discrete maximum principle are called monotone [14]
Extensive literature is devoted to the study of monotone difference schemes for linear elliptic and parabolic equations in the scalar case, for example
In this paper we have developed a theory of monotonicity for finite difference schemes approximating weakly coupled system of linear elliptic and quasilinear parabolic equations
Summary
Computational methods satisfying the discrete maximum principle are called monotone [14]. Monotonicity of these difference schemes are studied and a priori estimates of stability of the difference solution are established. For this purpose, the well-known idea of designing such schemes in the scalar case is used [15, 7, 9, 16, 4]
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