scholarly journals Exact Solutions for nonlinear partial differential equation by modified F-expansion method

2018 ◽  
Vol 10 (3) ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Expansion Method ◽  
Partial Differential

scholarly journals Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Xiao-Feng Yang ◽  
Yi Wei
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
Expansion Method ◽  
Partial Differential ◽  
The Kdv Equation ◽  
Compatible Condition ◽  
Ode Method ◽  
Bilinear Equation

The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. The KdV equation, Burgers equation, Boussinesq equation, and Sawada-Kotera equation are chosen to illustrate the validity of our method. We find that the underlying relation among the G′/G-expansion method, Hirota’s method, and HB method is a bilinear equation. The proposed method is also a standard and computable method, which can be generalized to deal with other types of NLPDE.

scholarly journals Exact solutions of (1+1)-Dimensional Kaup-Kupershmidt equation

2021 ◽  
Vol 12 (2) ◽  
pp. 3029-3031
Author(s):  
Anjali Verma, Et. al.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential

In this paper, we have obtained new analytical solutions of Kaup-Kupershmidt equation by using one method. We conclude that One method present a wider applicability for managing nonlinear partial differential equation. The solutions obtained in this paper are new.

scholarly journals Sinc-Galerkin method for solving hyperbolic partial differential equations

2018 ◽  
Vol 8 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Hyperbolic Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

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