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SOLUTIONS OF COMPLEX EQUATIONS WITH ADOMIAN DECOMPOSITION METHOD

Year 2017, Volume: 7 Issue: 1, 66 - 73, 01.06.2017

Abstract

In this study, fi rst order linear complex differential equations have been solved with adomian decomposition method.

References

  • Adomian,G.,(1988), A review of the decomposition method in applied mathematics, J. Math. Anal.Appl., 135, pp. 501-544.
  • Babolian,E., Biazar,J. and Islam,R., (2004), Solution of the system of ordinary differential equations by Adomian decomposition method, Appl. Math. Comput., 147, pp. 713-719.
  • Bildik,N. and Bayramoglu,H., (2005), The solution of two dimensional nonlinear differential equation by the Adomian decomposition method, Applied Mathematics and Computation, 163, pp. 519-524
  • Bougoffa,L., Mennouni,A. and Rach,R.C., (2013), Solving couchy integral equations of the first kind by the adomian decomposition method, Applied Mathematics and Computation, 219, pp. 4423-4433. [5] Bougoffa,L., Rach,R.C. and Mennouni,A., (2011), A convenient technigue for solving linear and non linear Abel integral equations by the Adomian decomposition method, Applied Mathematics and Computation, 218, pp. 1785-1793
  • Abdou,M.A., (2011), Solitary Solutions of Nonlinear Differential-difference Equations via Adomain Decomposition Method, International Journal of Nonlinear Science, 12(1), pp. 29-35
  • Momani,S. and Al-Khaled,K., (2005), Numerical solutions for systems of fractional differential equa- tions by the decomposition method, Applied Mathematics and Computation, 162, pp. 1351-1365
  • Parthiban,V. and Balachandran,K., (2013), Solutions of system of Fractional Partial Differential Equa- tions, Applications and Applied Mathematics, 8(1), pp. 289-304
  • Daftardar-Gejji,V. and Jafari,H., (2005), Adomian decomposition: a tool for solving a system of fractional differential equations, Journal of Mathematical Analysis and Applications 301(2) pp. 508- 518
  • Wazwaz,A.M., El Sayed,S.M., (2001), A new modification of the Adomian decomposition method for linear and nonlinear operators , Applied Mathematics and Computation, 122, pp. 393-405
  • Almazmumy,M., Hendi,F.A., Bakodah,H.O. and Alzumi,H., (2012), Recent Modifications of Ado- mian Decomposition Method for Initial Value Problem in Ordinary Differential Equations, American Journal of Computational Mathematics, 2, pp. 228-234
  • Rach,R., Adomian,G. and Meyers,R.E., (1992), A Modified Decomposition, Computers & Mathemat- ics with Applications, 23(1), pp. 17-23.
  • Wazwaz,A.M., (1999), A Reliable Modification of Adomian Decomposition Method, Applied Mathe- matics Computation, 102(1), pp. 77-86.
  • Luo,X.G., (2005), A Two-Step Adomian Decomposition Method, Applied Mathematics and Compu- tation, 170(1), pp. 570-583
  • Babolian,E. and Javadi,S., (2003), Restarted Adomian Method or Algebraic Equations, Applied Math- ematics and Computation, 146(2-3), pp. 533-541.
  • Babolian,E., Javadi,S. and Hosseini,S.G., (2004), Restarted Adomian Method for Integral Equations, Applied Mathematics and Computation, 153 (2), pp. 353-359.
  • Sinan,D. and Nejdet,B., (2014), Comparison of Adomian decomposition method and Taylor matrix method in solving different kinds of partial differential equations, International Journal of Modelling and Optimization, 4(4), pp. 292-298, .
  • Nejdet,B. and Sinan,D., (2015), Implementation of Taylor Collocation and Adomian Decomposition Method for Systems of Ordinary Differential Equations , 12th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 1648, AIP Publishing
  • Wazwaz,A.M., (2001), The modified decomposition method applied to unsteady flow of gas through a porous medium, Applied Mathematics and Computation, 118 (2-3) pp. 123-132
  • Hosseini,S.G., Babolian,E. and Abbasbandy,S., (2016) A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method, International Journal of Industrial Mathematics 8(3), pp. 177-184.
Year 2017, Volume: 7 Issue: 1, 66 - 73, 01.06.2017

Abstract

References

  • Adomian,G.,(1988), A review of the decomposition method in applied mathematics, J. Math. Anal.Appl., 135, pp. 501-544.
  • Babolian,E., Biazar,J. and Islam,R., (2004), Solution of the system of ordinary differential equations by Adomian decomposition method, Appl. Math. Comput., 147, pp. 713-719.
  • Bildik,N. and Bayramoglu,H., (2005), The solution of two dimensional nonlinear differential equation by the Adomian decomposition method, Applied Mathematics and Computation, 163, pp. 519-524
  • Bougoffa,L., Mennouni,A. and Rach,R.C., (2013), Solving couchy integral equations of the first kind by the adomian decomposition method, Applied Mathematics and Computation, 219, pp. 4423-4433. [5] Bougoffa,L., Rach,R.C. and Mennouni,A., (2011), A convenient technigue for solving linear and non linear Abel integral equations by the Adomian decomposition method, Applied Mathematics and Computation, 218, pp. 1785-1793
  • Abdou,M.A., (2011), Solitary Solutions of Nonlinear Differential-difference Equations via Adomain Decomposition Method, International Journal of Nonlinear Science, 12(1), pp. 29-35
  • Momani,S. and Al-Khaled,K., (2005), Numerical solutions for systems of fractional differential equa- tions by the decomposition method, Applied Mathematics and Computation, 162, pp. 1351-1365
  • Parthiban,V. and Balachandran,K., (2013), Solutions of system of Fractional Partial Differential Equa- tions, Applications and Applied Mathematics, 8(1), pp. 289-304
  • Daftardar-Gejji,V. and Jafari,H., (2005), Adomian decomposition: a tool for solving a system of fractional differential equations, Journal of Mathematical Analysis and Applications 301(2) pp. 508- 518
  • Wazwaz,A.M., El Sayed,S.M., (2001), A new modification of the Adomian decomposition method for linear and nonlinear operators , Applied Mathematics and Computation, 122, pp. 393-405
  • Almazmumy,M., Hendi,F.A., Bakodah,H.O. and Alzumi,H., (2012), Recent Modifications of Ado- mian Decomposition Method for Initial Value Problem in Ordinary Differential Equations, American Journal of Computational Mathematics, 2, pp. 228-234
  • Rach,R., Adomian,G. and Meyers,R.E., (1992), A Modified Decomposition, Computers & Mathemat- ics with Applications, 23(1), pp. 17-23.
  • Wazwaz,A.M., (1999), A Reliable Modification of Adomian Decomposition Method, Applied Mathe- matics Computation, 102(1), pp. 77-86.
  • Luo,X.G., (2005), A Two-Step Adomian Decomposition Method, Applied Mathematics and Compu- tation, 170(1), pp. 570-583
  • Babolian,E. and Javadi,S., (2003), Restarted Adomian Method or Algebraic Equations, Applied Math- ematics and Computation, 146(2-3), pp. 533-541.
  • Babolian,E., Javadi,S. and Hosseini,S.G., (2004), Restarted Adomian Method for Integral Equations, Applied Mathematics and Computation, 153 (2), pp. 353-359.
  • Sinan,D. and Nejdet,B., (2014), Comparison of Adomian decomposition method and Taylor matrix method in solving different kinds of partial differential equations, International Journal of Modelling and Optimization, 4(4), pp. 292-298, .
  • Nejdet,B. and Sinan,D., (2015), Implementation of Taylor Collocation and Adomian Decomposition Method for Systems of Ordinary Differential Equations , 12th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2014), 1648, AIP Publishing
  • Wazwaz,A.M., (2001), The modified decomposition method applied to unsteady flow of gas through a porous medium, Applied Mathematics and Computation, 118 (2-3) pp. 123-132
  • Hosseini,S.G., Babolian,E. and Abbasbandy,S., (2016) A new algorithm for solving Van der Pol equation based on piecewise spectral Adomian decomposition method, International Journal of Industrial Mathematics 8(3), pp. 177-184.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. Duz This is me

Publication Date June 1, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

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