A Variable Stepsize, Variable Order Family of Low Complexity

2021 ◽  
Vol 43 (3) ◽  
pp. A2130-A2160
Author(s):  
Victor DeCaria ◽  
Ahmet Guzel ◽  
William Layton ◽  
Yi Li
Keyword(s):  
Low Complexity ◽  
Variable Order ◽  
Variable Stepsize

On the zero stability of the variable order variable stepsize BDF-Formulas

1990 ◽  
Vol 57 (1) ◽  
pp. 39-50 ◽  
Author(s):  
M. Calvo ◽  
T. Grande ◽  
R. D. Grigorieff
Keyword(s):  
Variable Order ◽  
Variable Stepsize ◽  
Order Variable

scholarly journals Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator

2017 ◽  
Vol 890 ◽  
pp. 012045 ◽  
Author(s):  
Ahmad Fadly Nurullah Rasedee ◽  
Norizarina Ishak ◽  
Siti Raihana Hamzah ◽  
Hazizah Mohd Ijam ◽  
Mohamed Suleiman ◽  
...  
Keyword(s):  
Duffing Oscillator ◽  
Variable Order ◽  
Variable Stepsize ◽  
Order Variable

scholarly journals The solution of Riccati type differential equation by means of variable order variable stepsize backward difference method

2016 ◽  
Vol 2016 (1) ◽  
pp. 35-42
Author(s):  
Ahmad Fadly Nurullah b. Rasedee ◽  
Mohamed b. Suleiman ◽  
Ali Ahmadian ◽  
Zarina Bibi bt. Ibrahim ◽  
Khairil Iskandar b. Othman ◽  
...  
Keyword(s):  
Differential Equation ◽  
Difference Method ◽  
Variable Order ◽  
Variable Stepsize ◽  
Type Differential Equation ◽  
Order Variable

scholarly journals Solution for nonlinear Duffing oscillator using variable order variable stepsize block method

MATEMATIKA ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 165 ◽  
Author(s):  
Ahmad Fadly Nurullah Rasedee ◽  
Mohamad Hasan Abdul Sathar ◽  
Norizarina Ishak ◽  
Nur Shuhada Kamarudin ◽  
Muhamad Azrin Nazri ◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Duffing Oscillator ◽  
Computational Cost ◽  
Real Life ◽  
Multistep Method ◽  
Variable Order ◽  
Block Method ◽  
Step Size ◽  
Variable Stepsize

Real life phenomena found in various fields such as engineering, physics, biology and communication theory can be modeled as nonlinear higher order ordinary differential equations, particularly the Duffing oscillator. Analytical solutions for these differential equations can be time consuming whereas, conventional numerical solutions may lack accuracy. This research propose a block multistep method integrated with a variable order step size (VOS) algorithm for solving these Duffing oscillators directly. The proposed VOS Block method provides an alternative numerical solution by reducing computational cost (time) but without loss of accuracy. Numerical simulations are compared with known exact solutions for proof of accuracy and against current numerical methods for proof of efficiency (steps taken).

Sign in / Sign up

Export Citation Format

Share Document