64
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Saulyev'S Techniques For Solving A Parabolic Equation With A Non Linear Boundary Specification

Pages 257-265 | Published online: 15 Sep 2010

  • Cannon , J. R. and Lin , Y. 1990 . A Galerkin procedure for diffusion equation with boundary integral conditions . Intern. J. Engng. Sci. , 28 (7} ) : 579 – 587 .
  • Cannon , J. R. , Lin , Y. and Matheson , A. L. 1993 . The solution of the diffusion equation in two-space variables subject to the specification of mass . Appl. Anal. , 50 : 1 – 19 .
  • Cannon , J. R. and Van Der Hoek , J. 1986 . Diffusion subject to specification of mass . J. Math. Anal. Appl , 115 : 517 – 529 .
  • Cannon , J. R. , Lin , Y. and Wang , S. 1990 . An implicit finite difference scheme for the diffusion equation subject to mass specification . Intern. J. Engng. Sci. , 28 (7} ) : 573 – 578 .
  • Cannon , J. R. and Matheson , A. L. 1993 . A numerical procedure of diffusion subject to the specification of mass . Intern. J. Engng. Sci , 31 : 347 – 354 .
  • Cannon , J. R. 1984 . The one dimensional heat equation. Encyclopedia of Mathematics and its Applications , Vol. VoI. 23 , Men 10 Park, Calif. : Addison-Welsey .
  • Cannon , J. R. and Van Der Hoek , J. 1981 . The existence of a continuous dependence result for the solution of the heat equation subject to the specification of energy . BuIt. Un. Mat. Ital. Suppl , 1 : 253 – 282 .
  • Cannon , J. R. , Lin , Y. and Van Der Hoek , J. 1989 . A quasi-linear parabolic equation with nonlocal boundary condition . Rendiconti di Matematica, Serie VII, Roma , 9 : 239 – 264 .
  • Capasso , V and Kunisch , K. 1988 . A reaction-diffusion system arising in modeling man-environment diseases . Quart. Appl. Math. , 46 (3} ) : 431 – 449 .
  • Choi , Y. S. and Chan , K. Y. 1992 . A parabolic equation with nonlocal boundary conditions arising from electrochemistry . Nonlinear Analysis, Theory, Methods, and Applications , 18 (4} ) : 317 – 331 .
  • Day , W. A. 1982 . Existence of a property of solutions of the heat equation to linear thermoelasticity and other theories . Quart. Appl Math. , 40 : 319 – 330 .
  • Day , W. A. 1983 . A decreasing property of solutions of parabolic equations with applications to thermoelasticity . Quart. Appl. Math. , 41 : 468 – 475 .
  • Day , W. A. 1992 . Parabolic equations and thermodynamics . Quart. Appl Math. , 50 : 523 – 533 .
  • Dehghan , M. 1999 . Alternating direction implicit methods for two-dimensional diffusion with a non-local boundary condition . Intern. J. Computer Math. , 72 : 349 – 366 .
  • Gerald , C. F. and Wheatley , P. O. 1994 . Applied Numerical Analysis , 5th ed. , Addison-Wesley .
  • Kawohl , B. 1987 . Remark on a paper by W. A. Day on a maximum principle under non-local boundary conditions . Quart. Appl. Math. , 44 : 751 – 752 .
  • Lapidus , L. and Finder , G. F. 1982 . Numerical Solution of Partial Differential Equations in Science and Engineering , New York : Wiley .
  • Liu , Y. 1999 . Numerical solution of the heat equation with nonlocal boundary conditions . J. Comput Appl. Math. , 110 (1} ) : 115 – 127 .
  • Sun , Z. Z. 1996 . 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 .
  • Wang , S. 1990 . The numerical method for the heat conduction subject to moving boundary energy specification . Numerical Heat Transfer , 130 : 35 – 38 .
  • Yurchuk , N. I. 1986 . Mixed problem with an integral condition for certain parabolic equations . J. Diff. Eqs. , 22 : 2117 – 2126 .
  • Dehgan , M. 2002 . Numerical solution of the three-dimensional parabolic equation with an integral condition . Numer. Methods Partial Differential Eq. , 18 : 193 – 202 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.