Constuction of solitary solutions for nonlinear differential-difference equations via Adomain decomposition method

محورهای موضوعی : Applied Mathematics

M.A. Abdou ¹

1 - Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt.

تاریخ دریافت : 1394/07/08 تاریخ پذیرش : 1394/07/08 تاریخ انتشار : 1391/02/12

کلید واژه: Adomian decomposition method, Hybrid nonlinear difference equation, Relativistic Toda coupled nonlinear difference equation,

چکیده مقاله :

Here, Adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear differential difference equation and Relativistic Toda couplednonlinear differential-difference equation are chosen to illustrate the validity andthe great potential of the proposed method. Comparisons are made between theresults of the proposed method and exact solutions. The results show that theAdomian Decomposition Method is an attractive method in solving the nonlineardifferential difference equations. It is worthwhile to mention that theAdomian decomposition method is also easy to be applied to other nonlineardifferential difference equation arising in physics.

چکیده انگلیسی:

Here, Adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear differential difference equation and Relativistic Toda couplednonlinear differential-difference equation are chosen to illustrate the validity andthe great potential of the proposed method. Comparisons are made between theresults of the proposed method and exact solutions. The results show that theAdomian Decomposition Method is an attractive method in solving the nonlineardifferential difference equations. It is worthwhile to mention that theAdomian decomposition method is also easy to be applied to other nonlineardifferential difference equation arising in physics.