References
- A. Bouziani. On a class of parabolic equations with nonlocal boundary condition. Acad. Roy. Belg. Bull. Cl. Sci., 10:61–77, 1999.
- A. Bouziani, N. Merazga. Solution to a semilinear pseudoparabolic problem with integral condition. Electron. J. Differential Equations, 115:1–18, 2006.
- J. Cannon, A. Matheson. A numerical procedure for diffusion subject to the specification of mass. Internat. J. Engrg. Sci., 31(3):347–355, 1993. http://dx.doi.org/10.1016/0020-7225(93)90010-R.
- R. Čiegis. Parallel numerical algorithms for 3D parabolic problem with nonlocal boundary condition. Informatica, 17(3):309–324, 2006.
- R. Čiegis, A. Mirinavičius. On some finite difference schemes for solution of hyperbolic heat conduction problems. Cent. Eur. J. Math., 9(5):1164–1170, 2011. http://dx.doi.org/10.2478/s11533-011-0056-5.
- R. Čiegis, A. Štikonas, O. Štikonienė, O. Suboč. Stationary problems with nonlocal boundary conditions. Math. Model. Anal., 6(2):178–191, 2001. http://dx.doi.org/10.1080/13926292.2001.9637157.
- R. Čiegis, A. Štikonas, O. Štikonieneė, O. Suboč. Monotone finite-difference scheme for parabolical problem with nonlocal boundary conditions. Differ. Equ., 38(7):1027–1037, 2002. http://dx.doi.org/10.1023/A:1021167932414.
- R. Čiegis, N. Tumanova. Numerical solution of parabolic problems with nonlocal boundary conditions. Numer. Funct. Anal. Optim., 31(12):1318–1329, 2010. http://dx.doi.org/10.1080/01630563.2010.526734.
- D. Dai, Y. Huang. Nonlocal boundary problems for a third-order one-dimensional nonlinear pseudoparabolic equation. Nonlin. Anal., 66:179–191, 2007. http://dx.doi.org/10.1016/j.na.2005.11.021.
- G. Ekolin. Finite difference methods for a nonlocal boundary value problem for the heat equation. BIT, 31:245–261, 1991. http://dx.doi.org/10.1007/BF01931285.
- R.E. Ewing. Numerical solution of Sobolev partial differential equations. SIAM J. Numer. Anal., 12(3):345–363, 1975. http://dx.doi.org/10.1137/0712028.
- G. Fairweather, J.C. Lopez-Marcos. Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Adv. Comput. Math., 6:243–262, 1996. http://dx.doi.org/10.1007/BF02127706.
- W.H. Ford, T.W. Ting. Stability and convergence of difference approx-imations to pseudoparabolic partical differential equations. Math. Comput., 27(124):737–743, 1973. http://dx.doi.org/10.1090/S0025-5718-1973-0366052-4.
- A. Friedman. Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions. Quart. Appl. Math., 44:401–407, 1986.
- A.V. Gulin, V.A. Morozova, N.S. Udovichenko. Stability criterion for a family of nonlocal difference schemes. Differ. Equ., 46(7):2716–2732, 2010. http://dx.doi.org/10.1134/S0012266110070050..
- B. Gustafsson. High Order Difference Methods for Time Dependent PDE, volume 38 of Springer Ser. Comput. Math. Springer, Berlin, Heidelberg, New York, Tokyo, 2008.
- W. Hundsdorfer and J.G. Verwer. Numerical Solution of Time-Dependent Advection–Difusion–Reaction Equations, volume 33 of Springer Ser. Comput. Math. Springer, Berlin, Heidelberg, New York, Tokyo, 2003.
- J. Jachimavičienė. Explicit difference schemes for pseudoparabolic equation with integral condition. Liet. Mat. Rink., 53:36–41, 2012.
- J. Jachimavičienė, M. Sapagovas. Locally one-dimensional difference scheme for a pseudoparabolic equation with nonlocal conditions. Lith. Math. J., 52(1):53–61, 2012. http://dx.doi.org/10.1007/s10986-012-9155-7.
- J. Jachimavičienė, Ž. Jasevičiūtė and M. Sapagovas. The stability of finite-difference schemes for a pseudoparabolic equation with nonlocal conditions, Numer. Funct. Anal. Optim., 30(9):988–1001, 2009. http://dx.doi.org/10.1080/01630560903405412.
- H. Kalis, A. Buikis. Method of lines and finite difference schemes with the exact spectrum for solution the hyperbolic heat conduction equation. Math. Model. Anal., 16(2):220–232, 2011. http://dx.doi.org/10.3846/13926292.2011.578677.
- I. Lin, T. Zhang. Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions. J. Math. Anal. Appl., 165:180–191, 1992. http://dx.doi.org/10.1016/0022-247X(92)90074-N.
- A.A. Samarskii. The Theory of Difference Schemes. Marcel Dekker, Inc., New York, Basel, 2001.
- M. Sapagovas. On stability of finite-difference schemes for one-dimensional parabolic equations subject to integral condition. Obchysl. Prykl. Mat., 92:77–90, 2005.
- M. Sapagovas. On stability of finite difference schemes for nonlocal parabolic boundary value problems. Lith. Math. J., 48(3):339–356, 2008. http://dx.doi.org/10.1007/s10986-008-9017-5.
- M. Sapagovas, A. Štikonas. On the structure of the spectrum of a differential operator with a nonlocal condition. Differ. Equ., 41(7):1010–1018, 2005. http://dx.doi.org/10.1007/s10625-005-0242-y.
- P. Vabishchevich. On a new class of additive (splitting) operator difference schemes. Math. Comp., 81(277):267–276, 2012. http://dx.doi.org/10.1090/S0025-5718-2011-02492-0.
- V. Vodakhova. A boundary value problem with Nakhushev nonlocal condition for a certain pseudoparabolic moisture-transfer equation. Differ. Uravn., 18:280–285, 1982.