scholarly journals A finite difference scheme for solving the Timoshenko beam equations with boundary feedback

2007 ◽  
Vol 200 (2) ◽  
pp. 606-627 ◽  
Author(s):  
Fu-le Li ◽  
Zhi-zhong Sun
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Timoshenko Beam ◽  
Finite Difference Scheme ◽  
Boundary Feedback ◽  
Beam Equations

scholarly journals AN EFFICIENT FINITE DIFFERENCE SCHEME FOR THE NUMERICAL SOLUTION OF TIMOSHENKO BEAM MODEL

2021 ◽  
Vol 16 (5) ◽  
Author(s):  
Kamran Malik
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Timoshenko Beam ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Variable Load ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Step Size

We propose and implement a finite difference scheme for the numerical solution of the Timoshenko beam model without locking phenomenon. The averaging concept is used in approximating the function, and thus developing the scheme for elements. Finally, the system is discretized into the algebraic system using the proposed scheme and the numerical solution is attained. The numerical solutions are attained for a constant load and a variable load comprising linear and exponential functions. The mathematical model of the Timoshenko beam (TB) problem in the form of a boundary-value problem has been solved successfully for the rotation and displacement parameters. The results agree with other schemes in the literature for various values of the parameter and step size.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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