ls Reference List for MDM

Preface

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Glossary

Complete List of Publications for the Modified Decomposition Method

Monographs and textbooks

  1. Haldar, K., Decomposition Analysis Method in Linear and Nonlinear Differential Equations, Chapman and Hall/CRC, Boca Raton, FL, 2016, (Published October 16, 2015), Pp. 7-11, 23-25, 46-57, 63-67, 70-72, 75-76, 79-80, 82-83, 91-99, 105-106, 118-120, 158-163, 181-183, 193-204, Hardcover: ISBN-10: 1498716334, ISBN-13: 978-1498716338, eBook: ISBN: 9781498716345
  2. Serrano, S.E., Section 2.8: The Modified Decomposition Method (MDM), Section 3.10: The Modified Decomposition Method (MDM) for Nonlinear Equations, Section 4.9: The Modified Decomposition Method (MDM) for Nonlinear Systems, in: S.E. Serrano, Differential Equations: Applied Mathematical Modeling, Nonlinear Analysis, and Computer Simulation in Engineering and Science, HydroScience Inc., Ambler, Pennsylvania, 2016, Pp. 61-69, 134-142, 203-213, Hardcover: ISBN-10: 0988865211, ISBN-13: 978-0988865211, Paperback: ISBN-10: 098886522X, ISBN-13: 978-0988865228

A bibliography of the modified decomposition method (MDM)

Reference List for MDM, 1989

  1. Adomian, G. and Rach, R., Analytic parametrization and the decomposition method, Applied Mathematics Letters, 1989, Vol. 2, No. 4, pp. 311-313, https://doi.org/10.1016/0893-9659(89)90076-1

Reference List for MDM, 1991

  1. Adomian, G. and Rach, R., Transformation of series, Applied Mathematics Letters, 1991, Vol. 4, pp. 69--71. https://doi.org/10.1016/0893-9659(91)90058-4

Reference List for MDM, 1992

  1. Adomian, G. and Rach, R., Nonlinear transformation of series – Part II, Computers & Mathematics with Applications, 1992, Vol. 23, Issue 10, pp. 79--83, https://doi.org/10.1016/0898-1221(92)90058-P
  2. Adomian, G. and Rach, R., Inhomogeneous nonlinear partial differential equations with variable coefficients, Applied Mathematics Letters, 1992, Vol. 5, Issue 2, pp. 11--12; https://doi.org/10.1016/0893-9659(92)90101-E
  3. Adomian, G. and Rach, R., Modified decomposition solution of nonlinear partial differential equations, Applied Mathematics Letters, 1992, Vol. 5, Issue 6, pp. 29-30, https://doi.org/10.1016/0893-9659(92)90008-W
  4. Rach, R., Adomian, G., Meyers, R.E., A modified decomposition, Computers & Mathematics with Applications, 1992, Vol. 23, Issue 1, pp. 17--23; https://doi.org/10.1016/0898-1221(92)90076-T

Reference List for MDM, 1993

  1. Adomian, G. and Rach, R., Solution of nonlinear partial differential equations in one, two, three, and four dimensions, in: R.P. Agarwal, (Ed.), World Scientific Series in Applicable Analysis 2: Contributions in Numerical Mathematics, 1993, Pp. 1-13, https://doi.org/10.1142/9789812798886_0001

Reference List for MDM, 1994

  1. Abbaoui, K. and Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Computers & Mathematics with Applications, 1994, Vol. 28, Issue 5,, pp. 103-109, https://doi.org/10.1016/0898- 1221(94)00144-8
  2. Adomian, G. and Rach, R., Modified decomposition solution of linear and nonlinear boundary- value problems, Nonlinear Analysis: Theory, Methods and Applications, 1994, Vol. 23, No. 5, pp. 615-619, https://doi.org/10.1016/0362-546X(94)90240-2
  3. G. Adomian, Chapter 5: Modified Decomposition, Chapter 6: Applications of Modified Decomposition, Chapter 9: Boundary conditions at infinity, Chapter 12: Solution of the Duffing Equation, in: G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic, Dordrecht, 1994, Pp. 115-153, 154-189, 211-223, 236-287, ISBN-10: 079232644X , ISBN-13: 9780792326441, Hardcover: ISBN 978-0-7923-2644-1, Softcover: ISBN 978-90-481-4352-8, eBook: ISBN 978-94-015-8289-6

Reference List for MDM, 1995

  1. G. Adomian, G., Rach, R., Shawagfeh, N.T., On the analytic solution of the Lane-Emden equation, Foundations of Physics Letters, 1995, Vol. 8, No. 2, pp. 161-181; https://doi.org/10.1007/BF02187585

Reference List for MDM, 1997

  1. Adomian, G., Rach, R., Meyers, R.E., Numerical integration, analytic continuation and decomposition, Applied Mathematics and Computation, Vol. 88, 1997, Pp. 95-116, https://doi.org/10.1016/S0096- 3003(96)00052-5

Reference List for MDM, 2001

  2. Wazwaz, A.M., El-Sayed, S.M., A new modification of the Adomian decomposition method for linear and nonlinear operators, Applied Mathematics and Computation, 2001, Volume 122, Issue 3, 15 August 2001, Pages 393-405; https://doi.org/10.1016/S0096-3003(00)00060-6

Reference List for MDM, 2002

  1. Babolian, E., Biazar, J., Solution of nonlinear equations by modified adomian decomposition method, Applied Mathematics and Computation, 2002, Vol. 132, No. 1, pp. 167--172. doi: 10.1016/S0096-3003(01)00184-9

Reference List for MDM, 2003

  1. Abbasbandy, S., Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation, 2003, Vol. 145, pp. 887--893.

Reference List for MDM, 2005

  1. Jin, C. and Liu, M., A new modification of Adomiandecomposition method for solvinga kind of evolution equation, Applied Mathematics and Computation, 2005, Vol. 169, pp. 953--962.

Reference List for MDM, 2006

  1. Haldar, K., Application of modified decomposition method to Laplace equation in two dimensional polar coordinates, Bulletin of the Calcutta Mathematical Society., 2006, Vol. 98, No. 5, pp. 571-586,
  2. Hosseini, M.M. and Nasabzadeh, H. (2007), Modified Adomian decomposition method for specific second order ordinary differential equations, Applied Mathematics and Computation, 2007, Vol. 186 No. 1, pp. 117--123. https://doi.org/10.1016/j.amc.2006.07.094
  3. Wazwaz, A.-M., The modified decomposition method for analytic treatment of differential equations, Applied Mathematics and Computation, 2006, Volume 173, Issue 1, 1 February 2006, Pages 165--176; https://doi.org/10.1016/j.amc.2005.02.048

Reference List for MDM, 2008

  1. Haldar, K., Some exact solutions of linear fluid flow problems by modified decomposition method, Bulletin of the Calcutta Mathematical Society., 2008, Vol. 100, No. 3, pp. 283-300
  2. Hasan, Y.Q. and Zhu, L.M., Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations, Surveys in Mathematics and its Applications, 2008, Vol. 3, pp. 183--193.
  3. Hsu, J.C., Lai, H.Y., Chen, C.K., Free vibration of non-uniform Euler–Bernoulli beams with general elastically end constraints using Adomian modified decomposition method, Journal of Sound and Vibration, 2008, Volume 318, Issues 4–5, Pages 965-981; https://doi.org/10.1016/j.jsv.2008.05.010
  4. Lai, H.Y., Chen, C.K., Hsu, J.C., Free vibration of non-uniform Euler–Bernoulli beams by the Adomian modified decomposition method, CMES: Computer Modeling in Engineering & Sciences, Vol. 34, 2008, Pp. 87-116, http://www.techscience.com/doi/10.3970/cmes.2008.034.087.pdf

Reference List for MDM, 2009

  1. Hsu, J.C., Lai, H.Y., Chen, C.K., An innovative eigenvalue problem solver for free vibration of uniform Timoshenko beams by using the Adomian modified decomposition method, Journal of Sound and Vibration, 2009, Vol. 325, pp. 451-470, https://doi.org/10.1016/j.jsv.2009.03.015

Reference List for MDM, 2010

  1. Mao, Q. and Pietrzko, S., Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method, Journal of Sound and Vibration, Vol. 329, No. 11, 2010, Pp. 2068-2082. https://doi.org/10.1016/j.jsv.2009.12.016
  2. Mao, Q., & Pietrzko, S. (2010). Free vibration analysis of stepped beams by using Adomian decomposition method, Applied Mathematics and Computation, 217(7), 3429-3441. https://doi.org/10.1016/j.amc.2010.09.010

Reference List for MDM, 2011

  1. Duan, J.-S. and Rach, R., New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods, Applied Mathematics and Computation, Vol. 218, 2011, Pp. 2810-2828, https://doi.org/10.1016/j.amc.2011.08.024
  2. Mao, Q., Free vibration analysis of multiple-stepped beams by using Adomian decomposition method, Mathematical and Computer Modelling, Vol. 54, Nos. 1/2, 2011, Pp. 756-764. https://doi.org/10.1016/j.mcm.2011.03.019

Reference List for MDM, 2012

  1. Duan, J.-S. Chaolu, T., and Rach, R., Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method, Applied Mathematics and Computation, 2012, Volume 218, Issue 17, 1 May 2012, Pages 8370-8392; https://doi.org/10.1016/j.amc.2012.01.063
  2. Duan, J.-S. and Rach, R., Higher-order numeric Wazwaz–El-Sayed modified Adomian decomposition algorithms, Computers & Mathematics with Applications, 2012, Volume 63, Issue 11, June 2012, Pages 1557-1568; https://doi.org/10.1016/j.camwa.2012.03.050
  3. Duan, J.-S., Temuer, C.L., Rach, R., Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method, Applied Mathematics and Computation, Vol. 218, 2012, Pp. 8370-8392, https://doi.org/10.1016/j.amc.2012.01.063
  4. Hasan, Y.Q., Modified Adomian decomposition method for second ordersingular initial value problems, Advances in Computational Mathematics, 2012, Vol. 1, No. 2, pp. 94--99.
  5. López-Sandoval, E., Mello, A., Godina-Nava, J.J., Power SeriesSolution toNon-Linear Partial Differential Equationsof Mathematical Physics, 2012,
  6. Shahba, A., R. Attarnejad, R., Marvi, M.T., Shahriari, V., Free vibration analysis of non-uniform thin curved arches and rings using Adomian modified decomposition method, Arabian Journal for Science and Engineering, Vol. 37, 2012, pp. 965-976; https://doi.org/10.1007/s13369-012-0228-z
  7. Soroush, R., Koochi, A., Kazemi, A.S. and Abadyan, M. (2012), “Modeling the effect of van der Waals attraction on the instability of electrostatic cantilever and doubly-supported nano-beams using modified Adomian method”, International Journal of Structural Stability and Dynamics, 2012, Vol. 12, No. 5, https://doi.org/10.1142/S0219455412500368

Reference List for MDM, 2013

  1. Duan, J.-S., Rach, R., Wazwaz, A.-M., A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions, Applied Mathematical Modelling, 2013, Vol. 37, Issues 20-21, pp. 8687--8708.
  2. Duan, J.-S., Rach, R., Wazwaz, A.-M., A new modified Adomian decomposition method for higher-order nonlinear dynamical systems, CMES: Computer Modeling in Engineering & Sciences, 2013, Vol. 94, No. 1, 2013, pp. 77--118, http://www.techscience.com/doi/10.3970/cmes.2013.094.077.pdf
  3. Mao, Q., Application of Adomian Modified Decomposition Method to Free Vibration Analysis of Rotating Beams, Mathematical Problems in Engineering, Volume 2013, Article ID 284720, 10 pages; http://dx.doi.org/10.1155/2013/284720
  4. Rach, R., Wazwaz, A.-M., Duan, J.-S., A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations, Kybernetes, 2013, Vol. 42, No. 2, pp. 282--308, https://doi.org/10.1108/03684921311310611
  5. Wazwaz, A.-M., Rach, R., Duan, J.-S., The modified Adomian decomposition method and the noise terms phenomenon for solving nonlinear weakly-singular Volterra and Fredholm integral equations, Open Engineering, 2013, Vol. 3, Issue 4, ttps://doi.org/10.2478/s13531-013-0123-8
  6. Wazwaz, A.-M., Rach, R., Duan, J.-S., Adomian decomposition method for solving the Volterra integral form of the Lane–Emden equations with initial values and boundary conditions, Applied Mathematics and Computation, Volume 219, Issue 10, 15 January 2013, Pages 5004-5019; https://doi.org/10.1016/j.amc.2012.11.012

Reference List for MDM, 2014

  1. Bagheri, S., Nikkar, A., Ghaffarzadeh, H., Study of nonlinear vibrationof Euler-Bernoulli beams by using analytical approximate techniques, Latin American Journal of Solids and Structures, 2014, Vol. 11, pp. 154--168.
  2. Dalir, N., Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics, International Journal of Mathematics and Mathematical Sciences, Volume 2014, Article ID 793685, 7 pages http://dx.doi.org/10.1155/2014/793685
  3. Dib, A. Haiahem, A. Bou-Said, B., An analytical solution of the MHD Jeffery-Hamel flow by the modified Adomian decomposition method, Computers & Fluids, 102 (2014) 111-115. https://doi.org/10.1016/j.compfluid.2014.06.026
  4. Duan, J., Higher-order numeric solutions for nonlinear systems based on the Modified Decomposition Method, Journal of Applied Mathematics and Physics, 2014, ol. 2, pp. 1--7; http://dx.doi.org/10.4236/jamp.2014.2100
  5. Lin, Y. and Chen, C.-K., Modified Adomian decomposition method for double singular boundary value problem, Romanian Journal of Physics, 2014, Vol. 59, No. 5-6, pp. 443--453;
  6. Rabie, M.E.A. and Elzaki, T.M., A study of some systems of nonlinear partial differential equations by using Adomian and modified decomposition methods, African Journal of Mathematics and Computer Science Research, Vol. 7(6), pp. 61-67, October, 2014; doi: 10.5897/AJMCSR2014.0541 Article Number: 98918D947930
  7. Ramana, P.V. and Prasad, B.K.R., Modified Adomian Decomposition Method for Van der Pol equations, International Journal of Non-Linear Mechanics, 2014, Vol. 65, pp. 121--132.
  8. Zitoun, F.B., Solutions of linear and nonlinear partial differential equations with initial conditions and multivariate Faà di Bruno formula, [hal-00845788, version 1 - 9 Jan 2014.], 9 pages, 2014, , https://hal.archives-ouvertes.fr/hal-00845788/document

Reference List for MDM, 2015

  1. Duan, J.-S. and Rach, R., The degenerate form of the Adomian polynomials in the power series method for nonlinear ordinary differential equations, Journal of Mathematics and System Science, 2015, Volume 5, Pages 411--428, doi: 10.17265/2159-5291/2015.10.003
  4. Wattanasakulpong, N. and Chaikittiratana, A., Adomian-modified decomposition method for large-amplitude vibration analysis of stepped beams with elastic boundary conditions, Mechanics Based Design of Structures and Machines, Vol. 44, No. 3, 2015, Pp. 270-282. http://dx.doi.org/10.1080/15397734.2015.1055762

Reference List for MDM, 2016

  1. Adair, D. and Jaeger, M., Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method, Applied Mathematical Modelling, 2016, Vol. 40, Issue 4, pp. 3230-3241, https://doi.org/10.1016/j.apm.2015.09.097
  3. Serrano,S.E., Section 2.8: The Modified Decomposition Method (MDM), Section 3.10: The Modified Decomposition Method (MDM) for Nonlinear Equations, Section 4.9: The Modified Decomposition Method (MDM) for Nonlinear Systems, in: S.E. Serrano, Differential Equations: Applied Mathematical Modeling, Nonlinear Analysis, and Computer Simulation in Engineering and Science, HydroScience Inc., Ambler, Pennsylvania, 2016, Pp. 61-69, 134-142, 203-213, Hardcover: ISBN-10: 0988865211, ISBN-13: 978-0988865211, Paperback: ISBN-10: 098886522X, ISBN-13: 978-0988865228

Reference List for MDM, 2017

  1. Al-Mazmumy, M., Modified Decomposition Method by Adomian and Rach for Solving Nonlinear Volterra Integro-Differential Equations, Nonlinear Analysis and Differential Equations,, 2017, Vol. 5, No. 4, pp. 157--170; https://doi.org/10.12988/nade.2017.612101
  2. Az-Zo'bi, E.A. and Qousini, M.M., Modified Adomian-Rach decomposition method for solving nonlinear time-dependent IVPs, Applied Mathematical Sciences, 2017, Vol. 11, No. 8, pp. 387-395, https://doi.org/10.12988/ams.2017.714
  3. Duan, J.-S., R. Rach, R., Wazwaz, A.M., Higher-order numeric solutions of the Lane-Emden type equations derived from the multi-stage modified decomposition method, International Journal of Computer Mathematics, 2017, Vol. 94, No. 1, 2017, Pp. 197-215, https://doi.org/10.1080/00207160.2015.1100299
  4. Nuruddeen, R.I., Elzaki decomposition method and its applications in solving linear and nonlinear Schrodinger equations, Sohag Journal of Mathematics, 2017, Vol. 4, No. 2, pp. 31-35. http://dx.doi.org/10.18576/sjm/040201
  5. Sirisubtawee, S. and Kaewta, S., New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems, International Journal of Mathematics and Mathematical Sciences, 2017, Volume 2017, Article ID 5742965, 20 pages https://doi.org/10.1155/2017/57429652017,
  6. Sunday, J., Convergence analysis and implementation of Adomian decomposition method on second-order oscillatory problems, Asian Research Journal of Mathematics, 2017, Vol. 2, No. 5, pp. 1--12. Article no.ARJOM.32011

Reference List for MDM, 2018

  1. Adair, D. and Jaeger, M., Simulation of the vibrations of a non-uniform beam loaded with both a transversely and axially eccentric tip mass, International Journal of Computational Methods and Experimental Measurements, Vol. 6, No. 4, 2018, Pp. 679-690, https://doi.org/10.2495/CMEM- V6-N4-679-690
  2. Adair, D. and Jaeger, M., Vibration analysis of a uniform pre-twisted rotating Euler–Bernoulli beam using the modified Adomian decomposition method, Mathematics and Mechanics of Solids, Vol. 23, No. 9, Pp. 1345-1363, 2018. https://doi.org/10.1177/1081286517720843
  3. Daoud, Y. and Khidir, A.A., Modified Adomian decomposition method for solving the problem of boundary layer convective heat transfer, Propulsion and Power Research, 2018, Vol. 7, Issue 3, pp. 231--237.

Reference List for MDM, 2019

  1. Adair, D., Ibrayev, A., Tazabekova, A., Kim, J.R., Free vibrations with large amplitude of axially loaded beams on an elastic foundation using the Adomian modified decomposition method, Shock and Vibration, Vol. 2019, Article ID 3405075, 10 pages https://doi.org/10.1155/2019/3405075
  2. Adair, D. and Jaeger, M., Efficient calculation of the hingeless rotor blade flap-lag-torsion dynamics for helicopters, AIAA Scitech 2019 Forum, 7-11 January 2019, San Diego, California, AIAA 2019-1029, Session: Structural Dynamics of Beams, Plates, and Membranes II, Published Online: 6 Jan 2019, AIAA = American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2019-1029
  3. Alderremy, A., Elzaki, T.M., Chamekh, M., Modified Adomian Decomposition Method to solve generalized Emden–Fowler systems for singular IVP, Mathematical Problems in Engineering, 2019, Volume 2019, Article ID 6097095, 6 pages https://doi.org/10.1155/2019/6097095
  5. Shishesaz, M., Shariati, M., Yaghootian, A., Nonlocal elasticity effect on linear vibration of nano-circular plate using Adomian decomposition method, Journal of Applied and Computational Mechanics, 2019, Vol. 6, Issue 1, pp. 63--70; doi: 10.22055/jacm.2019.28504.1488