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A New Combined Homotopy-Laplace Decomposition Method for Solving DDEs of Order (1, 2)

R. Rangarajan|Ananth Kumar S. R.
장전수학회 (Jangjeon Mathematical Society)|2018.01|Advanced Studies in Contemporary Mathematics|제28권 제1호|pp. 13-25|DOI http://dx.doi.org/10.17777/ascm2017.28.13

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키워드

Laplace transformDifferential-difference equationIntegro-differential-difference equationAdomian polynomials
주제분류수학

초록

In the recent literature, nonlinear problems are solved by two powerful decomposition methods, namely, Laplace decomposition method and Homotopy analysis methods. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations of order (1, 2).

Abstract

In the recent literature, nonlinear problems are solved by two powerful decomposition methods, namely, Laplace decomposition method and Homotopy analysis methods. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations of order (1, 2).

참고문헌 (10)

  1. G. Adomian, "Solving Frontier Problems of Physics: The Decomposition Method" (1994), Kluwer Academic Publishers
  2. G. Adomian, "A review of the decomposition method and some recent results for nonlinear equation", Math. Comput. Modelling, 13(7), pp.17~43 (1992)
  3. S. R. Ananth Kumar, "Applicability of Laplace decomposition method for solving certain differential-difference equation of order (1,2)", Bulletin of the International Mathematical Virtual Institute, 3, pp.103~111 (2013)
  4. E. Babolian, "An efficient method for nonlinear fractional differential equations: Combination of the Adomian decomposition method and spectral method", Indian J. Pure Appl. Math., pp.1017~1028 (2014)
  5. D. Bahuguna, "A comparative study of numerical methods for solving an integro-differential equation", Computers and Mathematics with Applications, 57, pp.1485~1493 (2009)[DOI]
  6. R. Bellman, "Differential-Difference Equations" (1963), Academic press
  7. B. Deka, "Finite element method for a class of parabolic integro-differential equations with interfaces", Indian J. Pure Appl. Math., 44, pp.823~847 (2013)[DOI]
  8. A. Ghorbani, "He's Homotopy perturbation method for calculating Adomian polynomials", International Journal of Nonlinear Sciences and Numerical Simulation, 8(2), pp.229~232 (2007)
  9. S. Liao, "Beyond Perturbation. Introduction to Homotopy Analysis Method", pp.2004, Chapman and Hall
  10. A.M.Wazwaz, "Analytical Approximation and Pade Approximation for Volterra's population model", Appl. Math. and Comput., 100, pp.13~25 (1999)

관련 논문AI추천

Laplace decomposition method for solving certain differential-difference equations both of order 1Ananth Kumar S. R, R. Rangarajan장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제3호The reliable modified of Laplace adomian decomposition method to solve nonlinear interval Volterra-Fredholm integral equationsAhmed A. Hamoud, KIRTIWANT P. GHADLE강원경기수학회 · 한국수학논문집2017 · 제25권 제3호Homotopy analysis and Homotopy Pade methods for mixed Volterra-Fredholm integral equationsG. Hojjati, H. Kheiri, S. Fazeli장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제4호The use of variational iteration method to solve a nonlinear Volterra-Fredholm integro-differential equationSh. S. Behzadi장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제1호ANALYTICAL TECHNIQUES FOR SYSTEM OF TIME FRACTIONAL NONLINEAR DIFFERENTIAL EQUATIONS최준상, Devendra Kumar, Jagdev Singh, Ram Swroop대한수학회 · 대한수학회지2017 · 제54권 제4호Solutions of a class of singular second-order IVPs by variational homotopy perturbation methodM. Mahdavi, M. Matinfar장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제4호

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