Closed-form stiffness matrices for higher order tetrahedral finite elements

2012 ◽  
Vol 44 (1) ◽  
pp. 75-79 ◽  
Author(s):  
Sara E. McCaslin ◽  
Panos S. Shiakolas ◽  
Brian H. Dennis ◽  
Kent L. Lawrence
Keyword(s):  
Finite Elements ◽  
Closed Form ◽  
Higher Order ◽  
Stiffness Matrices

Closed-form stiffness matrices for the linear strain and quadratic strain tetrahedron finite elements

1992 ◽  
Vol 45 (2) ◽  
pp. 237-242 ◽  
Author(s):  
P.S. Shiakolas ◽  
R.V. Nambiar ◽  
K.L. Lawrence ◽  
W.A. Rogers
Keyword(s):  
Finite Elements ◽  
Closed Form ◽  
Linear Strain ◽  
Stiffness Matrices

On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

2020 ◽  
Vol 70 (3) ◽  
pp. 641-656
Author(s):  
Amira Khelifa ◽  
Yacine Halim ◽  
Abderrahmane Bouchair ◽  
Massaoud Berkal
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
Fibonacci Numbers ◽  
Higher Order ◽  
Real Numbers ◽  
Lucas Numbers ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

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