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BAZI SINIR DEĞER PROBLEMLERİ İÇİN YENİ ÜRETİCİ ÇEKİRDEKLER VE HOMOJENLEŞTİRME DÖNÜŞÜMLERİ

Year 2020, Volume: 19 Issue: 38, 234 - 243, 31.12.2020

Elif Nuray Yıldırım

Abstract

Lineer olmayan sınır değer problemleri fizikte ve matematikte önemli bir yer tutmaktadır. Problemlere dair çözüm yaklaşımları ise bir o kadar öneme haizdir. Bu çalışmada, bazı yeni üretici çekirdekli uzaylar inşa edilerek bu uzaylara ait üretici çekirdek fonksiyonları elde edildi. Üretici çekirdek teorisi gereği çalışılan denklemin ve denkleme ait sınır şartlarının muhakkak suretle homojen olması önemli olduğundan, homojen olmayan sınır değer problemleri özel dönüşüm fonksiyonları kullanılarak homojen hale getirildi.

Keywords

Üretici çekirdek fonksiyonları Sınır değer Problemleri Üretici çekirdek metodu Homojen olmayan adi diferansiyel denklemler

References

  • Aronszajn, N., (1950), “Theory of reproducing kernels”, Trans. Amer. Math. Soc. 68, 337-404.
  • Bergman, S., (1950), “The Kernel Function and Conformal Mapping”, American Math. Soc., New York.
  • Coddington, E. A., Levinson, N., (1972), “Theory of Ordinary Differential Equations”, Tata McGraw-Hill Publishing.
  • Cui, M. , Lin, Y., (2009), “Nonlinear numerical analysis in the reproducing kernel space”, New York: Nova Sci. Publ..
  • Daşcıoğlu, A., Yaslan, H., (2011), “The solution of high-order nonlinear ordinary differential equations by Chebshev series”, Appl. Math. Comput. 217 , 5658-5666.
  • Fox, L., Mayers, D. F., (1987), “Numerical Solution of Ordinary Differential Equations”, Chapman and Hall. Freihat, A., Abu-Gdairi, R., Khalil, H., Abuteen, E., Al-Smadi, M., Khan, R. A., (2016), “Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems”, American Jour. of App. Sci., 13, 501-510.
  • Hasan, Y. Q., Zhu, L. M., ( 2009), “Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method”, Com. in Nonlinear Sci. and Num. Simul., vol. 14, no. 6, pp. 2592-2596,

NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS

Year 2020, Volume: 19 Issue: 38, 234 - 243, 31.12.2020

Elif Nuray Yıldırım

Abstract

Nonlinear boundary value problems have a significant role in the science. The solution approximations are also important as much as problems. In this study, new reproducing kernel spaces are constructed and reproducing kernel functions have been obtained for some boundary value problems. In the reproducing kernel theory, it is higly important to study wih homogeneous differential equation with the homogeneous conditions. For this purpose, homogenizing transformation functions have been found and nonlinear nonhomogeneous problems transformed to the homogeneous form.

Keywords

reproducing kernel fucntion Boundary value problems Reproducing kernel method Nonhomogeneous ordinary differential equations

References

  • Aronszajn, N., (1950), “Theory of reproducing kernels”, Trans. Amer. Math. Soc. 68, 337-404.
  • Bergman, S., (1950), “The Kernel Function and Conformal Mapping”, American Math. Soc., New York.
  • Coddington, E. A., Levinson, N., (1972), “Theory of Ordinary Differential Equations”, Tata McGraw-Hill Publishing.
  • Cui, M. , Lin, Y., (2009), “Nonlinear numerical analysis in the reproducing kernel space”, New York: Nova Sci. Publ..
  • Daşcıoğlu, A., Yaslan, H., (2011), “The solution of high-order nonlinear ordinary differential equations by Chebshev series”, Appl. Math. Comput. 217 , 5658-5666.
  • Fox, L., Mayers, D. F., (1987), “Numerical Solution of Ordinary Differential Equations”, Chapman and Hall. Freihat, A., Abu-Gdairi, R., Khalil, H., Abuteen, E., Al-Smadi, M., Khan, R. A., (2016), “Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems”, American Jour. of App. Sci., 13, 501-510.
  • Hasan, Y. Q., Zhu, L. M., ( 2009), “Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method”, Com. in Nonlinear Sci. and Num. Simul., vol. 14, no. 6, pp. 2592-2596,
There are 7 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Elif Nuray Yıldırım 0000-0002-2934-892X

Publication Date December 31, 2020
Submission Date December 22, 2020
Published in Issue Year 2020 Volume: 19 Issue: 38

Cite

APA Nuray Yıldırım, E. (2020). NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, 19(38), 234-243.
AMA Nuray Yıldırım E. NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi. December 2020;19(38):234-243.
Chicago Nuray Yıldırım, Elif. “NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS”. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi 19, no. 38 (December 2020): 234-43.
EndNote Nuray Yıldırım E (December 1, 2020) NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi 19 38 234–243.
IEEE E. Nuray Yıldırım, “NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS”, İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, vol. 19, no. 38, pp. 234–243, 2020.
ISNAD Nuray Yıldırım, Elif. “NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS”. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi 19/38 (December 2020), 234-243.
JAMA Nuray Yıldırım E. NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi. 2020;19:234–243.
MLA Nuray Yıldırım, Elif. “NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS”. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, vol. 19, no. 38, 2020, pp. 234-43.
Vancouver Nuray Yıldırım E. NEW REPRODUCING KERNELS AND HOMOGENIZING TRANSFORMS FOR SOME BOUNDARY VALUE PROBLEMS. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi. 2020;19(38):234-43.
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