A new method for judging the computational stability of the difference schemes of nonlinear evolution equations

2000 ◽  
Vol 45 (15) ◽  
pp. 1358-1361 ◽  
Author(s):  
Wantao Lin ◽  
Zhongzhen Ji ◽  
Bin Wang ◽  
Xiaozhong Yang
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Difference Schemes ◽  
Nonlinear Evolution Equations ◽  
New Method ◽  
Computational Stability ◽  
The Difference

Role of parabolic viscosity in numerical analysis of derivative nonlinear evolution equations

1998 ◽  
Vol 2 ◽  
pp. 75-80
Author(s):  
Tadas Meškauskas ◽  
Feliksas Ivanauskas
Keyword(s):  
Numerical Analysis ◽  
Nonlinear System ◽  
Boundary Value Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Initial Conditions ◽  
Nonlinear Evolution Equations ◽  
Complex Vector ◽  
The Difference

We consider the difference schemes applied to a derivative nonlinear system of evolution equations. For the boundary-value problem with initial conditions ∂u/∂t = A ∂2u/∂x2 + B ∂u/∂x + f(x,u) + g(x,u) ∂u/∂x,    (t,x) ∈  (0, T] x (0, 1),u(t,0) = u(t,1) = 0,    t ∈ [0, T],u(0,x) = u(0)(x),    x ∈ (0, 1) we use the Crank-Nicolson discretization. A is complex and B – real diagonal matrixes; u, f and g are complex vector-functions. The analysis shows that proposed schemes are uniquely solvable, convergent and stable in a grid norm W22 if all (diagonal) elements in Re(A) are positive. This is true without any restriction on the ratio of time and space grid steps.

scholarly journals The Double Auxiliary Equations Method and its Application to Some Nonlinear Evolution Equations

2019 ◽  
pp. 1-11 ◽  
Author(s):  
A. A. Moussa ◽  
I. M. E. Abdelstar ◽  
A. K. Osman ◽  
L. A. Alhakim
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Evolution Equations ◽  
New Method ◽  
Long Wave ◽  
Rlw Equation

Throughout this article, symbolic computation will be used in order to construct a more general exact solutions of the nonlinear evolution equations through a new method called the double auxiliary equations' method, the method represent the study focus of this article. The method has proven applicable and practical through its applications to the generalized regularized long wave (RLW) equation and nonlinear Schrodinger equation.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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