An exact solution of fractional Euler-Bernoulli equation for a beam with fixed-supported and fixed-free ends

2021 ◽  
Vol 396 ◽  
pp. 125932
Author(s):  
Tomasz Blaszczyk ◽  
Jaroslaw Siedlecki ◽  
HongGuang Sun
Keyword(s):  
Exact Solution ◽  
Bernoulli Equation

scholarly journals A New Exact Solution of Burgers’ Equation with Linearized Solution

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Chun-Ku Kuo ◽  
Sen-Yung Lee
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Arbitrary Constant ◽  
Nonlinear Term ◽  
Burgers Equation ◽  
Integration Method ◽  
Direct Integration ◽  
Bernoulli Equation ◽  
Simplest Equation Method ◽  
Direct Integration Method

This paper considers a general Burgers’ equation with the nonlinear term coefficient being an arbitrary constant. Two identical solutions of the general Burgers’ equation are separately derived by a direct integration method and the simplest equation method with the Bernoulli equation being the simplest equation. The proposed exact solutions overcome the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. In addition, a general Cole-Hopf transform is introduced. Finally, the proposed derived solution is compared with the perturbation solution and other existing exact solutions. A new phenomenon, which we named “kink sliding,” is observed.

scholarly journals Using Bernoulli Equation to Solve Burger's Equation

2014 ◽  
Vol 11 (2) ◽  
pp. 202-206
Author(s):  
Baghdad Science Journal
Keyword(s):  
Exact Solution ◽  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Bernoulli Equation ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Adomian Decomposition ◽  
Better Than ◽  
Variation Iteration Method

In this paper we find the exact solution of Burger's equation after reducing it to Bernoulli equation. We compare this solution with that given by Kaya where he used Adomian decomposition method, the solution given by chakrone where he used the Variation iteration method (VIM)and the solution given by Eq(5)in the paper of M. Javidi. We notice that our solution is better than their solutions.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
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