Lin, Yanping; Tait, R. J. Finite-difference approximations for a class of nonlocal parabolic boundary value problems. (English) Zbl 0787.65060 J. Comput. Appl. Math. 47, No. 3, 335-350 (1993). From the authors’ summary: We consider finite difference approximations for a class of nonlocal parabolic boundary value problems which arise in thermoelasticity and poroelasticity. Approximations for both fixed and natural boundary conditions are considered together with an analysis of their stability. An example arising in testing poroelastic annular cylindrical samples is considered under various boundary conditions and for realistic values of the physical parameters. Reviewer: J.Albrycht (Poznań) Cited in 6 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 35K15 Initial value problems for second-order parabolic equations Keywords:numerical example; finite difference; nonlocal parabolic boundary value problems; thermoelasticity; poroelasticity; stability PDFBibTeX XMLCite \textit{Y. Lin} and \textit{R. J. Tait}, J. Comput. Appl. Math. 47, No. 3, 335--350 (1993; Zbl 0787.65060) Full Text: DOI References: [1] Cannon, J. R.; van der Hoek, J., An implicit finite difference scheme for the diffusion equation subject to the specification of mass in a portion of the domain, (Noye, J., Numerical Solutions of Partial Differential Equations (1982), North-Holland: North-Holland Amsterdam), 527-539 [2] Day, W. A., A decreasing property of solutions of a parabolic equation with applications to thermoelasticity, Quart. Appl. Math., 41, 468-475 (1983) · Zbl 0514.35038 [3] Detournay, E.; Carvalho, J. L., Application of the pressurized hollow poroelastic cylinder solution to the interpretation of laboratory burst experiments, (Khair, Rock Mechanics as a Guide for Efficient Utilization of Natural Resources (1989), Balkema: Balkema Rotterdam) [4] Y. Lin and R.J. Tait, On a class of nonlocal parabolic boundary value problems, Internat. J. Engrg. Sci., to appear.; Y. Lin and R.J. Tait, On a class of nonlocal parabolic boundary value problems, Internat. J. Engrg. Sci., to appear. · Zbl 0787.65060 [5] Rice, J. R.; Cleary, M. P., Some basic stress diffusion solutions for fluid-saturated porous media with compressible constituents, Rev. Geophys. Space Phys., 14, 2, 227-241 (1976) [6] Richtmeyer, R. D.; Morton, K. W., Difference Methods for Initial-Value Problems (1967), Wiley/Interscience: Wiley/Interscience New York · Zbl 0155.47502 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.