Korobitsyn, V. A. Covariant transformations of basis differential-difference schemes in a plane. (Russian, English) Zbl 1249.65139 Zh. Vychisl. Mat. Mat. Fiz. 51, No. 11, 2033-2041 (2011); translation in Comput. Math. Math. Phys. 51, No. 11, 1915-1922 (2011). Summary: Consistent difference approximations to differential operators in vector and tensor analysis are constructed in curvilinear coordinates in a plane by applying the basis operator method. They are obtained as a transformation of basis approximations in a Cartesian coordinate system. For the continuum mechanics equations in Lagrangian variables, this approach yields theoretically justified differential-difference schemes whose conservation laws correspond to the continuous case. Cited in 1 Document MSC: 65L03 Numerical methods for functional-differential equations 34K34 Hybrid systems of functional-differential equations 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010) 65L12 Finite difference and finite volume methods for ordinary differential equations Keywords:consistent difference approximations; Cartesian coordinate system; basis operator method; differential-difference schemes PDFBibTeX XMLCite \textit{V. A. Korobitsyn}, Zh. Vychisl. Mat. Mat. Fiz. 51, No. 11, 2033--2041 (2011; Zbl 1249.65139); translation in Comput. Math. Math. Phys. 51, No. 11, 1915--1922 (2011) Full Text: DOI