Algorithms for solving linear, non-linear differential and differential-difference equations by approximating the solution to polynomials

2014 ◽  
Vol 5 (3) ◽  
pp. 236
Author(s):  
Sameh Abdelwahab Nasr Eisa
Keyword(s):  
Difference Equations ◽  
Non Linear ◽  
Linear Differential

scholarly journals A transformation to linearity of some non-linear differential-difference equations

1982 ◽  
Vol 23 (4) ◽  
pp. 416-419
Author(s):  
A. J. Bracken
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Non Linear ◽  
Differential Difference Equation ◽  
Linear Differential

AbstractThe problem of solving a differential-difference equation with quadratic non-linearities of a certain type is reduced to the problem of solving an associated linear differential-difference equation.

scholarly journals Further study on solutions of some non-linear homogeneous differential equations in connection to Brück conjecture

2021 ◽  
Vol 29 (2) ◽  
Author(s):  
DILIP CHANDRA PRAMANIK ◽  
KAPIL ROY
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Linear Differential Equations ◽  
Linear Complex ◽  
Non Linear ◽  
Complex Differential Equations ◽  
Sharing Function ◽  
Linear Differential ◽  
Brück Conjecture

In this paper, using the theory of complex differential equations, we study the solution of some non-linear complex differential equations in connection to Brück conjecture which generalized some earlier results due to Pramanik, D. C. and Biswas, M., On solutions of some non-linear differential equations in connection to Bruck conjecture, Tamkang J. Math., 48 (2017), No. 4, 365–375; and Wang, H., Yang, L-Z. and Xu, H-Y., On some complex differential and difference equations concerning sharing function, Adv. Diff. Equ., 2014, 2014:274.

scholarly journals GDTM-Padé technique for the non-linear differential-difference equation

2013 ◽  
Vol 17 (5) ◽  
pp. 1305-1310
Author(s):  
Jun-Feng Lu
Keyword(s):  
Difference Equation ◽  
Solitary Wave ◽  
Difference Equations ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Approximate Solutions ◽  
Lattice Equation ◽  
Non Linear ◽  
Differential Difference Equation ◽  
Linear Differential

This paper focuses on applying the GDTM-Pad? technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

scholarly journals Darboux transform and conservation laws of new differential-difference equations

2020 ◽  
Vol 24 (4) ◽  
pp. 2519-2527
Author(s):  
Sheng Zhang ◽  
Dongdong Liu
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Spectral Problem ◽  
Difference Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Darboux Transforms

Darboux transforms, exact solutions and conservation laws are important topics in thermal science and other fields as well. In this paper, the new non-linear differential-difference equations associated a discrete linear spectral problem are studied analytically. Firstly, the Darboux transform of the studied equations is constructed, and exact solutions are then obtained. Finally, infinite many conservation laws are derived.

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