Variable-order variable-step algorithms for second-order systems. Part 2: The codes

1988 ◽  
Vol 26 (1) ◽  
pp. 55-80 ◽  
Author(s):  
I. Gladwell ◽  
R. M. Thomas
Keyword(s):  
Second Order ◽  
Variable Order ◽  
Variable Step ◽  
Order Variable ◽  
Second Order Systems

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

2020 ◽  
Vol 11 (01) ◽  
pp. 2050001
Author(s):  
Lei Zhang ◽  
Chaofeng Zhang ◽  
Mengya Liu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Multistep Method ◽  
Second Order ◽  
Order Derivative ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step ◽  
The Stability

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

scholarly journals ℋ∞ Control Tunning to Guarantee the Output Performance of LTI Second-Order Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 4611-4616
Author(s):  
Ramón I. Verdés ◽  
Luis T. Aguilar ◽  
Yury Orlov
Keyword(s):  
Second Order ◽  
Output Performance ◽  
Second Order Systems
Sign in / Sign up

Export Citation Format

Share Document