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Erratum:

Year 2023, Volume: 16 Issue: 1, 295 - 296, 31.03.2023

Hakkı Duru Baransel Güneş

The original article was published on March 24, 2019. https://dergipark.org.tr/en/pub/erzifbed/issue/43859/479466

Erratum Note

In this corrigendum, it is aimed to correct some typos of the paper entitled “Parçalı Düzgün Şebekede Singüler Pertürbe Özellikli Lineer Olmayan Reaksiyon Difüzyon Problemleri İçin Nümerik Çözümler” [Erzincan University Journal of Science and Technology, 12(1) (2019), 425-436].

Abstract

References

  • Amiraliyev, G., Duru H., 2002. “Nümerik Analiz”, Pegem Yayıncılık.
  • Amiraliyev G. M., Mamedov Y.D.,1995. “Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations”, Tr. J. of Math., 19, 207-222.
  • Auchmutyi, J. F. G., Nicolis, G., 1976. Bulletin of Mathematical Biology. Bifurcation analysis of reaction-diffusion equations, 8:325-350.
  • Boglaev, I. P., 1984. Approximate solution of a nonlinear boundary value problem with a small parameter fort he highest-order differential. U.S.S.R. Comput. Maths. Math. Phys., 24(6):30-35.
  • Cantrell, R. S., Cosner, C., 2003. Spatial Ecology via Reaction-Diffusion Equations, Department of Mathematics, University of Miami, U.S.A.
  • Chaplain, M. A. J., 1995. “Reaction-diffusion prepatterning and its potential role in tumour invasion”. Journal of Biological Systems, 3(4):929-936.
  • Fife, P. C., 1979. “Mathematical Aspects of Reacting and Diffusing Systems”, Springer.
  • Gatenby, R. A., Gawlinski E.T., 1996. “A Reaction-Diffusion Model Cancer Research”, 56: 5745-5753.
  • Grindrod, P., 1991. Patterns and Wawes: “The Theory And Applications of Reaction-Diffusion Equations”, Clerandon Press.
  • Harrison, L. G., 1993. “Kinetic Theory of Living Pattern”, Cambridge University Press.
  • Holmes, E. E. et al., 1994. “Partial Differential Equations in Ecology: Spatial Interactions and Population Dynamics”. Ecology 75(1):17-29.
  • Kerner, B. S., Osipov, V.V., 1994. “Autosolitons: A New Approach to Problems of Self-Organization and Turbulence”, Kluwer Academic Publishers.
  • Kopteva, N., Stynes, M., 2004. “Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solitions”. Applied Numerical Mathematics 51: 273-288.
  • Mei, Z., 2000. “Numerical Bifurcation Analysis for Reaction-Diffusion Equations”, Springer, Berlin.
  • Meinhardt, H., 1982. “Models of Biological Pattern Formation”, Academic Press, London.
  • Mikhailov, A. S., 1990. “Foundations of Synergetics I, Distributed Active Systems”, Springer.
  • Murray, J. D., 1986. “On the spatial spread of rabies among foxes”. Proc. R. Soc. Lond. B, 229 (1225): 111-150.
  • Murray, J. D., 2013. “Mathematical Biology”, Springer Science&Business Media, 17: 436-450.
  • Ruuth, J. S., 1995. “Implicit-explicit methods for reaction-diffusion problems in pattern formation”. Journal of Mathematical Biology, volume 34, Issue 2, pp 148-176.
  • Samarskii, A.A., 2001. “The Theory of Difference Schemes”. Moscow M.V. Lomonosov State University, Russia.
  • Sherratt, J. A., Murray, J.D., 1990. “Models of epidermal wound healing”. Proc. R. Soc. Lond. B, 241:29-36.
  • Sherratt, J. A., Nowak, M.A., 1992. “Oncogenes, anti-oncogenes and the Immume response to cancer: A mathematical model”. Proc. R. Soc. Lond. B, 248(1323): 261-271.
  • Skellam, J. G., 1991. “Random Dispersal in Theoretical Populations”. Bulletin of Mathematical Biology, 53( ½ ): 135-165.
  • Smoller, J., 1994. Shock Waves and Reaction Diffusion Equations, Springer.
  • Turing, A. M., 1952. “The chemical basis of morphogenesis”, Philosopical Transactions of the Royal Society of London Series B, 237(641): 37-72, University of Manchester, Biological Sciences.

Erratum: Parçalı Düzgün Şebekede Singüler Pertürbe Özellikli Lineer Olmayan Reaksiyon Difüzyon Problemleri İçin Nümerik Çözümler

Year 2023, Volume: 16 Issue: 1, 295 - 296, 31.03.2023

Hakkı Duru Baransel Güneş

The original article was published on March 24, 2019. https://dergipark.org.tr/en/pub/erzifbed/issue/43859/479466

Erratum Note

Abstract

Bu
çalışmada singüler pertürbe özellikli lineer olmayan reaksiyon-difüzyon sınır
değer problemi ele alınmıştır. Kalan terimi integral biçiminde olan ve baz
fonksiyonu içeren interpolasyon kuadratür kuralları kullanılarak parçalı düzgün
şebeke üzerinde fark şeması kurulmuştur. Sunulan metodun kararlı olduğu
gösterilmiş ve yakınsaklık analizi yapılmıştır. Kurulan metodun yaklaşık çözüme
düzgün yakınsadığı gösterilmiştir. Nümerik sonuçların teorik sonuçları
desteklediği örnek üzerinde gösterilmiştir.

Keywords

Diferansiyel denklem Fark şeması Parçalı düzgün şebeke Singüler pertürbasyon

References

  • Amiraliyev, G., Duru H., 2002. “Nümerik Analiz”, Pegem Yayıncılık.
  • Amiraliyev G. M., Mamedov Y.D.,1995. “Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations”, Tr. J. of Math., 19, 207-222.
  • Auchmutyi, J. F. G., Nicolis, G., 1976. Bulletin of Mathematical Biology. Bifurcation analysis of reaction-diffusion equations, 8:325-350.
  • Boglaev, I. P., 1984. Approximate solution of a nonlinear boundary value problem with a small parameter fort he highest-order differential. U.S.S.R. Comput. Maths. Math. Phys., 24(6):30-35.
  • Cantrell, R. S., Cosner, C., 2003. Spatial Ecology via Reaction-Diffusion Equations, Department of Mathematics, University of Miami, U.S.A.
  • Chaplain, M. A. J., 1995. “Reaction-diffusion prepatterning and its potential role in tumour invasion”. Journal of Biological Systems, 3(4):929-936.
  • Fife, P. C., 1979. “Mathematical Aspects of Reacting and Diffusing Systems”, Springer.
  • Gatenby, R. A., Gawlinski E.T., 1996. “A Reaction-Diffusion Model Cancer Research”, 56: 5745-5753.
  • Grindrod, P., 1991. Patterns and Wawes: “The Theory And Applications of Reaction-Diffusion Equations”, Clerandon Press.
  • Harrison, L. G., 1993. “Kinetic Theory of Living Pattern”, Cambridge University Press.
  • Holmes, E. E. et al., 1994. “Partial Differential Equations in Ecology: Spatial Interactions and Population Dynamics”. Ecology 75(1):17-29.
  • Kerner, B. S., Osipov, V.V., 1994. “Autosolitons: A New Approach to Problems of Self-Organization and Turbulence”, Kluwer Academic Publishers.
  • Kopteva, N., Stynes, M., 2004. “Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solitions”. Applied Numerical Mathematics 51: 273-288.
  • Mei, Z., 2000. “Numerical Bifurcation Analysis for Reaction-Diffusion Equations”, Springer, Berlin.
  • Meinhardt, H., 1982. “Models of Biological Pattern Formation”, Academic Press, London.
  • Mikhailov, A. S., 1990. “Foundations of Synergetics I, Distributed Active Systems”, Springer.
  • Murray, J. D., 1986. “On the spatial spread of rabies among foxes”. Proc. R. Soc. Lond. B, 229 (1225): 111-150.
  • Murray, J. D., 2013. “Mathematical Biology”, Springer Science&Business Media, 17: 436-450.
  • Ruuth, J. S., 1995. “Implicit-explicit methods for reaction-diffusion problems in pattern formation”. Journal of Mathematical Biology, volume 34, Issue 2, pp 148-176.
  • Samarskii, A.A., 2001. “The Theory of Difference Schemes”. Moscow M.V. Lomonosov State University, Russia.
  • Sherratt, J. A., Murray, J.D., 1990. “Models of epidermal wound healing”. Proc. R. Soc. Lond. B, 241:29-36.
  • Sherratt, J. A., Nowak, M.A., 1992. “Oncogenes, anti-oncogenes and the Immume response to cancer: A mathematical model”. Proc. R. Soc. Lond. B, 248(1323): 261-271.
  • Skellam, J. G., 1991. “Random Dispersal in Theoretical Populations”. Bulletin of Mathematical Biology, 53( ½ ): 135-165.
  • Smoller, J., 1994. Shock Waves and Reaction Diffusion Equations, Springer.
  • Turing, A. M., 1952. “The chemical basis of morphogenesis”, Philosopical Transactions of the Royal Society of London Series B, 237(641): 37-72, University of Manchester, Biological Sciences.
There are 25 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Hakkı Duru 0000-0002-3179-3758

Baransel Güneş 0000-0002-3265-8881

Early Pub Date March 29, 2023
Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 16 Issue: 1

Cite

APA Duru, H., & Güneş, B. (2023). Parçalı Düzgün Şebekede Singüler Pertürbe Özellikli Lineer Olmayan Reaksiyon Difüzyon Problemleri İçin Nümerik Çözümler. Erzincan University Journal of Science and Technology, 16(1), 295-296. https://doi.org/10.18185/erzifbed.1228865
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