The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Homotopy-Laplace Decomposition Method to Solve Nonlinear Differential-difference Equations


Affiliations
1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India
2 Department of Mathematics, S.S.S.S. Govt. First Grade College, Channagiri, Davangere - 577 213, India
     

   Subscribe/Renew Journal


In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. 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.

Keywords

Differential-Difference Equation, Integro-Differential-Difference Equation, Laplace Transform, Adomian Polynomials, Laplace Decomposition Method and Homotopy Analysis Method.
Subscription Login to verify subscription
User
Notifications
Font Size


  • G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston and London, 1994.

  • G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Math.Comput.Modelling, 13(7) (1992), 17-43.

  • S. R. Ananth Kumar, Some studies on differential equations applicable to differential-difference equations, Ph. D. thesis, University of Mysore, 2014.

  • S. R. Ananth Kumar and R. Rangarajan, Applicability of Laplace decomposition method for solving certain differential-difference equation of order (1,2), Bulletin of the International Mathematical Virtual Institute, 3 (2013), 103-111.

  • E. Babolian and J. Biazar, Solution of nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation, 132 (2002), 167-172.

  • E. Babolian and A. Davari, Numerical implementation of Adomian decomposition method for linear Volterra integral equations of the second kind, Applied Mathematics and Computation, 165(1) (2005), 223-227.

  • E. Babolian, A. R. Vahidi and A. Shoja, An efficient method for nonlinear fractional differential equations: Combination of the Adomian decomposition method and spectral method, Indian J. Pure Appl. Math., (2014), 1017-1028.

  • D. Bahuguna, A. Ujlayan and D. N. Pandey, A comparative study of numerical methods for solving an integro-differential equation, Computers and Mathematics with Applications, 57 (2009), 1485-1493.

  • R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic press, New York, 1963.

  • B. Deka and R. C. Deka, Finite element method for a class of parabolic integro-differential equations with interfaces, Indian J. Pure Appl. Math., (44) (2013), 823-847.

  • A. Ghorbani and J. S. Nadja, He's Homotopy perturbation method for calculating Adomian polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 8(2) (2007), 229-232.

  • S. Liao, Beyond Perturbation:Introduction to Homotopy Analysis Method, Chapman and Hall/CRC, New York, 2004.

  • Mohamed M. Mousa and Aidarkhan Kaltayev, Homotopy perturbation method for solving nonlinear Differential-Difference Equations, Verlag der Zeitschrift fur Naturforschung, (2010), 511-517.

  • Peter J. Collins, Differential and Integral Equations, Oxford University Press, 2010.

  • R. Rangarajan and S. R. Ananth Kumar, Laplace decomposition methods for solving certain class of differential-difference equations, Journal of the Indian Math. Soc., 81 (2014), 01-11.

  • A. M. Wazwaz, Analytical Approximation and Pade Approximation for Volterra's population model, Appl. Math. and Comput., 100 (1999), 13-25.


Abstract Views: 309

PDF Views: 1




  • Homotopy-Laplace Decomposition Method to Solve Nonlinear Differential-difference Equations

Abstract Views: 309  |  PDF Views: 1

Authors

R. Rangarajan
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India
S. R. Ananth Kumar
Department of Mathematics, S.S.S.S. Govt. First Grade College, Channagiri, Davangere - 577 213, India

Abstract


In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. 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.

Keywords


Differential-Difference Equation, Integro-Differential-Difference Equation, Laplace Transform, Adomian Polynomials, Laplace Decomposition Method and Homotopy Analysis Method.

References