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Solution of the different typesof partial differantial equations using differantial transform and adomian decomposition methods

Year 2013, Volume: 3 Issue: 1, 8 - 26, 01.06.2013

Abstract

In this study, the Differential Transform Method (DTM) and Adomian’sDecomposition Method (ADM) are applied to certain linear and non-linear partialdifferential equations

References

  • Zhou, J.K., 1986. Differential transformation and its Application for Electrical Circuit, Huazhong University Press, Wuhan, China.
  • Arıkoglu, A., 2004. Application of differential transforms method to linear-nonlinear engineering problems, MS thesis, Istanbul Technical University.
  • Arıkoglu, A. and Ozkol, I., 2005. Solution of boundary value problems for integro- differential equations by using differential transform method. Applied Mathematics and Computations, 168(2): 1145-1158.
  • Arıkoglu, A. and Ozkol, I., 2006. Solution of difference equations by using differential transform method. Applied Mathematics and Computations, 174(2): 1216-1228.
  • Catal, S., 2008. Solution of free vibration equations of beam on elastic soil by using differential transform method. Applied Mathematical Modeling, 32: 1744-1757.
  • Catal, S., 2012a. Response of forced Euler-Bernoulli beams using differential transform method. Structural Engineering and Mechanics, 42(1): 95-119.
  • Catal, S., 2012b. Some of semi analytical methods for Blasius problem. AM Computer
  • Science and Communications Applied Mathematics, 3(7), 724-728.
  • Wazwaz, A.M., 1998. A comparison between Adomian decomposition method and Taylor series method in the series solutions. Applied Mathematics and Computations, 97: 37-44.
  • Wazwaz, A.M., 1999. A reliable modification of Adomian decomposition method. Applied Mathematics and Computations, 102: 77-86 .
  • Wazwaz, A.M., 2000. A new algorithm for calculating Adomian polynomials for nonlinear operators. Applied Mathematics and Computations, 11: 53-69.
  • Singh, N. and Kumar, M., 2011. Adomian Decomposition Method for Solving Higher Order Boundary Value Problems. Mathematical Theory and Modeling, 2(1), (online).
  • Bougoffa, L., Rach, R.C., and El-Manouni, S., 2013. A convergence analysis of the Adomian Decomposition Method for an abstract Cauchy Problem of a system of first-order nonlinear differential equations. International Journal of Computer Mathematics, 90(2): 360-375.
  • Bokhari, A.H., Mohammed, G., Mustafa, M.T., and Zaman, F.D., 2009. Adomian Decomposition Method for a nonlinear heat equation with temperature dependent thermal properties, Hindawi Publishing Corporation, Mathematical Problems in Engineering, doi:10.1155/2009/926086.
  • Jang, M.J., Chen, C.L., Liu, Y.C., 2000. On solving the initial value problems using differential transformation method. Applied Mathematics and Computations, 115, 145-160. [15] Chen, C.L. and Liu, Y.C., 1998. Solution of two-point boundary value problems using the differential transformation method. Journal of Optimization Theory and Applications, 91: 23-35.
  • Adomian, G., 1986. Nonlinear Stochastic Operator Equations, Academic Press, Orlando, FL.
  • Adomian, G., 1994. Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston.
  • Adomian, G. and Rach R., 1990. Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations. Applied Mathematics and Computations, 19: 9-12.
  • Adomian, G. and Rach R., 1993. Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition. Journal of Applied Mathematics, 174: 118-137.
  • Jang, M.J.,Chen, C.L., Liu, Y.C., 2001. Two-dimensional differential transform for partial differential equations. Applied Mathematics and Computations, 121: 261-270.

DİFERANSİYEL DÖNÜŞÜM VE ADOMIAN AYRIŞTIRMA YÖNTEMLERİ İLE FARKLI TİPTE KISMİ DIFERANSİYEL DENKLEMLERİN ÇÖZÜMLERİ

Year 2013, Volume: 3 Issue: 1, 8 - 26, 01.06.2013

Abstract

Bu çalışmada, Diferansiyel Dönüşüm Metodu (DTM) ve Adomian Ayrıştırma Metodu (ADM) uygulanarak belirli doğrusal ve doğrusal olmayan kısmi diferansiyel denklemlerin nümerik-analitik çözümleri sunulmuştur.

References

  • Zhou, J.K., 1986. Differential transformation and its Application for Electrical Circuit, Huazhong University Press, Wuhan, China.
  • Arıkoglu, A., 2004. Application of differential transforms method to linear-nonlinear engineering problems, MS thesis, Istanbul Technical University.
  • Arıkoglu, A. and Ozkol, I., 2005. Solution of boundary value problems for integro- differential equations by using differential transform method. Applied Mathematics and Computations, 168(2): 1145-1158.
  • Arıkoglu, A. and Ozkol, I., 2006. Solution of difference equations by using differential transform method. Applied Mathematics and Computations, 174(2): 1216-1228.
  • Catal, S., 2008. Solution of free vibration equations of beam on elastic soil by using differential transform method. Applied Mathematical Modeling, 32: 1744-1757.
  • Catal, S., 2012a. Response of forced Euler-Bernoulli beams using differential transform method. Structural Engineering and Mechanics, 42(1): 95-119.
  • Catal, S., 2012b. Some of semi analytical methods for Blasius problem. AM Computer
  • Science and Communications Applied Mathematics, 3(7), 724-728.
  • Wazwaz, A.M., 1998. A comparison between Adomian decomposition method and Taylor series method in the series solutions. Applied Mathematics and Computations, 97: 37-44.
  • Wazwaz, A.M., 1999. A reliable modification of Adomian decomposition method. Applied Mathematics and Computations, 102: 77-86 .
  • Wazwaz, A.M., 2000. A new algorithm for calculating Adomian polynomials for nonlinear operators. Applied Mathematics and Computations, 11: 53-69.
  • Singh, N. and Kumar, M., 2011. Adomian Decomposition Method for Solving Higher Order Boundary Value Problems. Mathematical Theory and Modeling, 2(1), (online).
  • Bougoffa, L., Rach, R.C., and El-Manouni, S., 2013. A convergence analysis of the Adomian Decomposition Method for an abstract Cauchy Problem of a system of first-order nonlinear differential equations. International Journal of Computer Mathematics, 90(2): 360-375.
  • Bokhari, A.H., Mohammed, G., Mustafa, M.T., and Zaman, F.D., 2009. Adomian Decomposition Method for a nonlinear heat equation with temperature dependent thermal properties, Hindawi Publishing Corporation, Mathematical Problems in Engineering, doi:10.1155/2009/926086.
  • Jang, M.J., Chen, C.L., Liu, Y.C., 2000. On solving the initial value problems using differential transformation method. Applied Mathematics and Computations, 115, 145-160. [15] Chen, C.L. and Liu, Y.C., 1998. Solution of two-point boundary value problems using the differential transformation method. Journal of Optimization Theory and Applications, 91: 23-35.
  • Adomian, G., 1986. Nonlinear Stochastic Operator Equations, Academic Press, Orlando, FL.
  • Adomian, G., 1994. Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston.
  • Adomian, G. and Rach R., 1990. Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations. Applied Mathematics and Computations, 19: 9-12.
  • Adomian, G. and Rach R., 1993. Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition. Journal of Applied Mathematics, 174: 118-137.
  • Jang, M.J.,Chen, C.L., Liu, Y.C., 2001. Two-dimensional differential transform for partial differential equations. Applied Mathematics and Computations, 121: 261-270.
There are 20 citations in total.

Details

Primary Language Turkish
Journal Section Review Articles
Authors

S. Çatal This is me

Seval Catal This is me

Publication Date June 1, 2013
Submission Date March 1, 2015
Published in Issue Year 2013 Volume: 3 Issue: 1

Cite

APA Çatal, S., & Catal, S. (2013). DİFERANSİYEL DÖNÜŞÜM VE ADOMIAN AYRIŞTIRMA YÖNTEMLERİ İLE FARKLI TİPTE KISMİ DIFERANSİYEL DENKLEMLERİN ÇÖZÜMLERİ. Ordu Üniversitesi Bilim Ve Teknoloji Dergisi, 3(1), 8-26.