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DIFFERENTIAL TRANSFORM METHOD FOR SOLVING A CLASS OF SINGULAR TWO-POINT BOUNDARY VALUE PROBLEMS

Year 2006, Volume: 1 Issue: 1, 70 - 76, 01.06.2006

Abstract

This paper applies the differential transform method to search for semi numerical-analytical solutions of a class of singular two-point boundary value problems. To make clear and illustrate the features and capabilities of the presented method, four examples are carried out. The results demonstrate the computational efficiency and reliability of the method. 

References

  • AGARWAL RP, 1986. Boundary Value Problems for High Order Differential Equations, World Scientific, Singapore.
  • ASCHER U, MATTHEIJ RMM, RUSSELL RD, 1998. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ.
  • CHAWLA MM, KATTI CP, 1984. A finite difference method for a class of singular two point boundary value problems, IMA Journal of Numerical Analysis, 4 , 457-466.
  • ÇAĞLAR N, ÇAĞLAR H, 2006. B-spline solution of singular boundary value problems, Applied Mathematics & Computation, in press.
  • ERIKSON K, THOMEE V, 1984. Galerkin methods for singular boundary value problems in one space dimension, Mathematics of Computation, 42 , 345-367.
  • GUSTAFSSON B, 1973. A numerical method for solving singular boundary value problems, Numerische Mathematik, 21, 328-344.
  • IYENGAR SRK, JAIN PC, 1987. Spline finite difference methods for singular two point boundary value problems, Numerische Mathematik, 50, 363-376.
  • JAMET P, 1970. On the convergence of finite difference approximations to one dimensional singular boundary value problems, Numerische Mathematik, 14, 355-378.
  • RAVI KANTH ASV, REDDY YN, 2003. A numerical method for singular boundary value problems via Chebyshev economization, Applied Mathematics & Computation, 146, 691-700.
  • RAVI KANTH ASV, REDDY YN, 2005. Cubic spline for a class of singular two-point boundary value problems, Applied Mathematics & Computation, 170, 733-740.
  • RAVI KANTH ASV, REDDY YN, 2004. Higher order finite difference method for a class of singular boundary value problems, Applied Mathematics & Computation, 155, 249-258.
  • RUSSELL RD, SHAMPINE LF, 1975. Numerical method for singular boundary value problems, SIAM. Journal of Numerical Analysis, 12, 13-36.
  • ZHOU JK, 1986. Differential Transformation and Its Applications for Electrical Circuits (in Chinese). Huazhong University Press, Wuhan, China.

BİR TÜR TEKİL İKİ-NOKTA SINIR DEĞER PROBLEMLERİNİN DİFERANSİYEL DÖNÜŞÜM METODU İLE ÇÖZÜMÜ

Year 2006, Volume: 1 Issue: 1, 70 - 76, 01.06.2006

Abstract

 Bu makale, bir tür tekil iki-nokta sınır değer problemlerinin yarı sayısal-analitik çözümlerinin diferansiyel dönüşüm yöntemi ile elde edilişini ele almaktadır. Yöntemin özelliklerini açığa vurmak ve işlerliğini örneklendirmek için dört örnek ele alındı. Elde edilen sonuçlar, metodun hesaplanabilirlik açısından güvenilirliğini ve etkinliğini ortaya koymaktadır. 

References

  • AGARWAL RP, 1986. Boundary Value Problems for High Order Differential Equations, World Scientific, Singapore.
  • ASCHER U, MATTHEIJ RMM, RUSSELL RD, 1998. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ.
  • CHAWLA MM, KATTI CP, 1984. A finite difference method for a class of singular two point boundary value problems, IMA Journal of Numerical Analysis, 4 , 457-466.
  • ÇAĞLAR N, ÇAĞLAR H, 2006. B-spline solution of singular boundary value problems, Applied Mathematics & Computation, in press.
  • ERIKSON K, THOMEE V, 1984. Galerkin methods for singular boundary value problems in one space dimension, Mathematics of Computation, 42 , 345-367.
  • GUSTAFSSON B, 1973. A numerical method for solving singular boundary value problems, Numerische Mathematik, 21, 328-344.
  • IYENGAR SRK, JAIN PC, 1987. Spline finite difference methods for singular two point boundary value problems, Numerische Mathematik, 50, 363-376.
  • JAMET P, 1970. On the convergence of finite difference approximations to one dimensional singular boundary value problems, Numerische Mathematik, 14, 355-378.
  • RAVI KANTH ASV, REDDY YN, 2003. A numerical method for singular boundary value problems via Chebyshev economization, Applied Mathematics & Computation, 146, 691-700.
  • RAVI KANTH ASV, REDDY YN, 2005. Cubic spline for a class of singular two-point boundary value problems, Applied Mathematics & Computation, 170, 733-740.
  • RAVI KANTH ASV, REDDY YN, 2004. Higher order finite difference method for a class of singular boundary value problems, Applied Mathematics & Computation, 155, 249-258.
  • RUSSELL RD, SHAMPINE LF, 1975. Numerical method for singular boundary value problems, SIAM. Journal of Numerical Analysis, 12, 13-36.
  • ZHOU JK, 1986. Differential Transformation and Its Applications for Electrical Circuits (in Chinese). Huazhong University Press, Wuhan, China.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Makaleler
Authors

Vedat Ertürk

Publication Date June 1, 2006
Published in Issue Year 2006 Volume: 1 Issue: 1

Cite

IEEE V. Ertürk, “DIFFERENTIAL TRANSFORM METHOD FOR SOLVING A CLASS OF SINGULAR TWO-POINT BOUNDARY VALUE PROBLEMS”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 1, no. 1, pp. 70–76, 2006.