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Mathematical Modelling and Analysis Volume 5, 2000 - Issue 1
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Original Articles

The estimates of accuracy of difference schemes for the nonlinear heat equation with weak solution

B.S. Jovanović Faculty of Mathematics, University of Belgrade, Studentski trg 16, Belgrade, 11001, Yugoslavia E-mail: [email protected]
,
P.P. Matus Institute of Mathematics, NAS of Belarus, Surganov St. 11, Minsk, 220072, Belarus E-mail: [email protected]‐net.by
&
V.S. Shchehlik Institute of Mathematics, NAS of Belarus, Surganov St. 11, Minsk, 220072, Belarus E-mail: [email protected]‐net.by
Pages 86-96 | Received 30 Aug 1999, Published online: 14 Oct 2010

References

  • Gavrilyuk , I. P. , Lazarov , R. D. , Makarov , V. L. and Pirnazarov , S. P. 1983 . Estimates of the convergence rate of difference solutions to solutions of the second boundary value problem for fourth order equation at minimal requirements to smoothness . Doklady AN USSR , : 6 – 9 . Ser. A, (in Russian)
  • Lions , J. L. and Magenes , E. 1968 . Problèmes aux limites non homogènes et applications , Paris : Dunod .
  • Makarov , V. L. and Slushaenko , N. V. 1983 . Consistent estimates of the rate of convergence of a mesh method for quasilinear elliptic equations with large Lipschitz constants . Differents. uravneniya , 19 (7) : 1219 – 1226 . (in Russian)
  • Matus , P. P. , Moskal'kov , M. N. and Shchehlik , V. S. 1995 . Consistent estimates for rate of convergence of the grid method for a second‐order nonlinear equation with generalized solutions . Differents. uravneniya , 31 (7) : 1249 – 1256 . (in Russian)
  • Samarskii , A. A. 1983 . Theory of difference schemes , Moscow : Nauka . (in Russian)
  • Samarskii , A. A. 1984 . Investigation of the accuracy of difference schemes for problems with generalized solutions. Current problems in mathematical physics and numerical mathematics , 174 – 183 . Moscow : Nauka . (in Russian)
  • Samarskii , A. A. , Lazarov , R. D. and Makarov , V. L. 1987 . Finite difference schemes for differential equations with generalized solutions , Moscow : Vysshaya shkola . (in Russian)
  • Samarskii , A. A. , Matus , P. P. , Jovanovich , B. S. and Shchehlik , V. S. 1997 . Finite difference schemes on time‐adaptive meshes for parabolic equations with generalized solutions . Differentsial'nye uravneniya , 33 (7) : 975 – 984 . (in Russian)
  • Samarskii , A. A. , Vabishchevich , P. N. and Matus , P. P. 1998 . Finite difference schemes with operator factors Minsk (in Russian)
  • Shchehlik , V. S. 1995 . Analysis of a difference scheme approximating the third boundary value problem for a second‐order nonlinear differential equation . Zh. vychisl. mat. mat. fiz , 37 (8) : 951 – 957 . (in Russian)
  • Matus , P. P. 1993 . Vesti ANB. , : 15 – 21 . (in Russian)

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