[1] |
Allegretto, W.; Lin, Y.; Zhou, A.: A box scheme for coupled systems resulting from micro-sensor thermistor problems. Dynam discr continuous impulse syst 5, 209-223 (1999) · Zbl 0979.78023 |

[2] |
Ang, W. T.: A method of solution for the one-dimensional heat equation subject to a nonlocal condition. SEA bull math 26, No. 2, 197-203 (2002) |

[3] |
Ang WT. Numerical solution of a non classical parabolic problem, an integro-differential approach. Appl Math Comput, in press. |

[4] |
Jr., G. W. Batten: Second-order correct boundary conditions for the numerical solution of the mixed boundary problem for parabolic equations. Math comput 17, 405-413 (1963) · Zbl 0133.38601 |

[5] |
Berzins, M.; Fuzerland, R. M.: Developing software for time-dependent problems using the method of lines and differential algebraic integrators. Appl numer math 5, No. 1, 375-397 (1989) · Zbl 0679.65071 |

[6] |
Boutayeb, A.; Chetouani, A.: Global extrapolation of numerical methods for solving a parabolic problem with nonlocal boundary conditions. Int J comput math 80, 789-797 (2003) · Zbl 1047.65080 |

[7] |
Bouziani, A.: On a class of parabolic equations with a nonlocal boundary condition. Acad R belg bull cl sci 10, 61-77 (1999) · Zbl 1194.35200 |

[8] |
Bouziani, A.: On the solvability of parabolic and hyperbolic problems with a boundary integral condition. Int J math math sci 31, No. 4, 201-213 (2002) · Zbl 1011.35002 |

[9] |
Bouziani, A.: On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification. Abstr appl anal 10, 573-589 (2003) · Zbl 1031.35051 |

[10] |
Cahlon, B.; Kulkrani, D. M.; Shi, P.: Stepwise stability for the heat equation with a nonlocal constraint. SIAM J numer anal 32, No. 2, 571-593 (1995) · Zbl 0831.65094 |

[11] |
Cannon, J. R.: The solution of the heat equation subject to the specification of energy. Quart appl math 21, 155-160 (1963) · Zbl 0173.38404 |

[12] |
Cannon, J. R.: The one dimensional heat equation. Encyclopedia of mathematics and its applications 23 (1984) |

[13] |
Cannon, J. R.; Matheson, A. L.: A numerical procedure for diffusion subject to the specification of mass. Int J eng sci 31, No. 3, 347-355 (1993) · Zbl 0773.65069 |

[14] |
Cannon, J. R.; Prez-Esteva, S.; Van Der Hoek, J.: A Galerkin procedure for the diffusion equation subject to the specification of mass. SIAM J num anal 24, 499-515 (1987) · Zbl 0677.65108 |

[15] |
Cannon, J. R.; Van Der Hoek, J.: Implicit finite difference scheme for the diffusion of mass in porous media. Numerical solution of partial differential equations, 527-539 (1982) |

[16] |
Cannon, J. R.; Van Der Hoek, J.: Diffusion subject to specification of mass. J math anal appl 115, 517-529 (1986) · Zbl 0602.35048 |

[17] |
Cannon, J. R.; Van Der Hoek, J.: The one phase Stefan problem subject to the specification of energy. J math anal appl 86, 281-289 (1982) · Zbl 0508.35074 |

[18] |
Cannon, J. R.; Van Der Hoek, J.: The classical solution of the one-dimensional two-phase Stefan problem with energy specification. Ann di mat pura ed appl 130, No. 4, 385-398 (1982) · Zbl 0493.35080 |

[19] |
Cannon, J. R.; Lin, Y.; Van Der Hoek, J.: A quasilinear parabolic equation with nonlocal boundary conditions. Rendicoti di math roma 9, 239-264 (1989) · Zbl 0726.35065 |

[20] |
Cannon, J. R.; Lin, Y.; Wang, S.: An implicit finite difference scheme for the diffusion equation subject to the specification of mass. Int J eng sci 28, No. 7, 573-578 (1990) · Zbl 0721.65046 |

[21] |
Cannon, J. R.; Lin, Y.: A Galerkin procedure for diffusion equations with boundary integral conditions. Int J eng sci 28, No. 7, 579-587 (1990) · Zbl 0721.65054 |

[22] |
Cannon, J. R.; Yin, H. M.: On a class of non-classical parabolic problems. Different equat 79, 266-288 (1989) · Zbl 0702.35120 |

[23] |
Cannon, J. R.; Yin, H. M.: An iteration procedure for a class of integro-differential equations of parabolic type. J integral equat appl 2, 31-47 (1989) |

[24] |
Capasso, V.; Kunisch, K.: A reaction-diffusion system arising in modeling man-environment diseases. Quart appl math 46, 431-449 (1988) · Zbl 0704.35069 |

[25] |
Choi, Y. S.; Chan, K. Y.: A parabolic equation with nonlocal boundary conditions arising from electrochemistry. Nonlinear anal theory methods appl 18, No. 4, 317-331 (1992) · Zbl 0757.35031 |

[26] |
Cushman, J. H.: Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Transp porous media 13, 123-138 (1993) |

[27] |
Cushman, J. H.; Xu, H.; Deng, F.: Nonlocal reactive transport with physical and chemical heterogeneity: localization error. Water resour res 31, 2219-2237 (1995) |

[28] |
Cushman, J. H.; Ginn, T. R.: Nonlocal dispersion in media with continuously evolving scales of heterogeneity. Transp porous media 13, 123-138 (1993) |

[29] |
Dagan, G.: The significance of heterogeneity of evolving scales to transport in porous formations. Water resour res 13, 3327-3336 (1994) |

[30] |
Day, W. A.: Existence of a property of solutions of the heat equation subject to linear thermoelasticity and other theories. Quart appl math 40, 319-330 (1982) · Zbl 0502.73007 |

[31] |
Day, W. A.: Parabolic equations and thermodynamics. Quart appl math 50, 523-533 (1992) · Zbl 0794.35069 |

[32] |
Day, W. A.: A decreasing property of solutions of a parabolic equation with applications to thermoelasticity and other theories. Quart appl math 41, 468-475 (1983) · Zbl 0514.35038 |

[33] |
Deckert, K. L.; Maple, C. G.: Solutions for diffusion equations with integral type boundary conditions. Proc iowa acad sci 70, 345-361 (1963) · Zbl 0173.12803 |

[34] |
Dehghan, M.: Numerical solution of a parabolic equation with non-local boundary specifications. Appl math comput 145, 185-194 (2003) · Zbl 1032.65104 |

[35] |
Dehghan, M.: The use of Adomian decomposition method for solving the one-dimensional parabolic equation with non-local boundary specifications. Int J comput math 81, 25-34 (2004) · Zbl 1047.65089 |

[36] |
Deng, K.: Comparison principle for some nonlocal problems. Quart appl math 50, No. 3, 517-522 (1992) · Zbl 0777.35006 |

[37] |
Diaz, C.; Fairweather, G.; Keast, P.: Fortran package for solving certain almost block diagonal linear systems by modified alternate row and column elimination. ACM trans math software 9, 358-375 (1983) · Zbl 0516.65013 |

[38] |
Ekolin, G.: Finite difference methods for a non-local boundary value problem for the heat equation. Bit 31, No. 2, 245-255 (1991) · Zbl 0738.65074 |

[39] |
Ewing, R. E.; Lazarov, R. D.; Lin, Y.: Finite volume element approximations of nonlocal in time one-dimensional flows in porous media. Computing 64, 157-182 (2000) · Zbl 0969.76052 |

[40] |
Ewing, R. E.; Lazarov, R. D.; Lin, Y.: Finite volume element approximations of nonlocal reactive flows in porous media. Numer methods partial different equat 16, 285-311 (2000) · Zbl 0961.76050 |

[41] |
Ewing, R. E.; Lin, T.: A class of parameter estimation techniques of fluid flow in porous media. Adv water resour 14, 89-97 (1991) |

[42] |
Fairweather, G.; Saylor, R. D.: The reformulation and numerical solution of certain nonclassical initial-boundary value problems. SIAM J sci stat comput 12, No. 1, 127-144 (1991) · Zbl 0722.65062 |

[43] |
Fairweather, G.; Lopez-Marcos, J. C.: Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions. Adv comput math 6, 243-262 (1996) · Zbl 0868.65068 |

[44] |
Fairweather G, Lopez-marcos JC, Boutayeb A, Orthogonal spline collocation for a quasilinear parabolic problem with a nonlocal boundary condition, in press. |

[45] |
Friedman, A.: Monotonic decay of solutions of parabolic equation with nonlocal boundary conditions. Quart appl math 44, 401-407 (1986) · Zbl 0631.35041 |

[46] |
Gumel, A. B.: On the numerical solution of the diffusion equation subject to the specification of mass. J aust math soc ser B 40, 475-483 (1999) · Zbl 0962.65078 |

[47] |
Ionkin, N. I.: Solution of a boundary value problem in heat conduction with a non-classical boundary condition. Different equat 13, 204-211 (1977) · Zbl 0403.35043 |

[48] |
Ionkin, N. I.: Stability of a problem in heat transfer theory with a non-classical boundary condition. Different equat 16, 911-914 (1980) · Zbl 0431.35045 |

[49] |
Ionkin, N. I.; Furleov, D. G.: Uniform stability of difference schemes for a nonlocal nonself-adjoint boundary value problem with variable coefficients. Different equat 27, 820-826 (1991) · Zbl 0818.65081 |

[50] |
Ionkin, N. I.; Moiseev, E. I.: A problem for heat transfer equation with two-point boundary condition. Different equat 15, 1284-1295 (1979) · Zbl 0415.35032 |

[51] |
Kamynin, L. I.: A boundary value problem in the theory of heat conduction with a non-classical boundary condition. USSR comput math math phys 4, 33-59 (1964) |

[52] |
Kacur, J.; Van Keer, R.: On the numerical solution of semilinear parabolic problems in multicomponent structures with Volterra operators in the transmission conditions and in the boundary conditions. Z angew math mech 75, No. 2, 91-103 (1995) |

[53] |
Lapidus, L.; Pinder, G. F.: Numerical solution of partial differential equations in science and engineering. (1982) · Zbl 0584.65056 |

[54] |
Lardner, R. W.: Stability of the numerical solution of a parabolic system with integral subsidiary conditions. Comput math appl 19, 41-46 (1990) · Zbl 0693.65066 |

[55] |
Lees, M.: A priori estimates for the solutions of difference approximations to parabolic partial differential equations. Duke J math 27, 297-311 (1960) · Zbl 0092.32803 |

[56] |
Lin Y, Parabolic partial differential equations subject to non-local boundary conditions, PhD dissertation. Department of Pure and Applied Mathematics, Washington State University, 1988. |

[57] |
Liu, Y.: Numerical solution of the heat equation with nonlocal boundary conditions. J comput appl math 110, No. 1, 115-127 (1999) · Zbl 0936.65096 |

[58] |
Makarov, V. L.; Kulyev, D. T.: Solution of a boundary value problem for a quasi-linear parabolic equation with nonclassical boundary conditions. Different equat 21, 296-305 (1985) · Zbl 0573.35048 |

[59] |
Murthy, A. S. V.; Verwer, J. G.: Solving parabolic integro-differential equations by an explicit integration method. J comput appl math 39, 121-132 (1992) · Zbl 0746.65102 |

[60] |
Pani, A. K.: A finite element method for a diffusion equation with constrained energy and nonlinear boundary conditions. J aust math soc ser B 35, 87-102 (1993) · Zbl 0797.65073 |

[61] |
Pluschke, V.; Weber, F.: The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition. Comment math univ carolina 40, No. 1, 13-38 (1999) · Zbl 1060.35528 |

[62] |
Renardy, M.; Hrusa, W.; Nohel, J. A.: Mathematical problems in viscoelasticity. (1987) |

[63] |
Saadatmandi, A.; Razzaghi, M.: A tau method approximation for the diffusion equation with nonlocal boundary conditions. Int J comput math 81, No. 11, 1427-1432 (2004) · Zbl 1063.65110 |

[64] |
Samarskii, A. A.: Some problems in differential equations theory. Different equat 16, 1221-1228 (1980) |

[65] |
Sapagovas, M.; Chegis, R. Yu.: On some boundary value problems with a nonlocal condition. Different equat 23, 858-863 (1987) · Zbl 0641.34014 |

[66] |
Shelukhin, V. V.: A non-local in time model for radionuclides propagation in Stokes fluids, dynamics of fluids with free boundaries. Siberian russ acad sci, inst hydrodynam 107, 180-193 (1993) |

[67] |
Shi, P.: Weak solution to an evolution problem with a nonlocal constraint. SIAM J math anal 24, No. 1, 46-58 (1993) · Zbl 0810.35033 |

[68] |
Shi, P.; Shillor, M.: Design of contact patterns in one-dimensional thermoelasticity, theoretical aspects of industrial design. (1992) |

[69] |
Sun, Z. Z.: A second-order accurate finite difference scheme for a class of nonlocal parabolic equations with natural boundary conditions. J comput appl math 76, 137-146 (1996) · Zbl 0873.65129 |

[70] |
Twizell, E. H.: Computational methods for partial differential equations. (1984) · Zbl 0546.65062 |

[71] |
Wang, S.; Lin, Y.: A numerical method for the diffusion equation with nonlocal boundary specifications. Int J eng sci 28, No. 6, 543-546 (1990) · Zbl 0718.76096 |

[72] |
Wang, S.; Lin, Y.: A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equations. Inverse problems 5, 631-640 (1989) · Zbl 0683.65106 |

[73] |
Wang, S.: A numerical method for the heat equation subject to moving boundary energy specification. Numer heat transfer 130, 35-38 (1990) |

[74] |
Yurchuk, N. I.: Mixed problem with an integral condition for certain parabolic equations. Different equat 22, 1457-1463 (1986) · Zbl 0654.35041 |

[75] |
Dehghan, M.: On the numerical solution of the diffusion equation with a nonlocal boundary condition. Math probl eng 2003, 81-92 (2003) · Zbl 1068.65115 |

[76] |
Dehghan, M.: The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure. Int J comput math 81, 979-989 (2004) · Zbl 1056.65099 |

[77] |
Dehghan, M.: On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numer meth partial different equat 21, 24-40 (2005) · Zbl 1059.65072 |