A Variable-step-size Block Predictor-corrector Method for Ordinary Differential Equations

2017 ◽  
Vol 10 (2) ◽  
pp. 96-101 ◽  
Author(s):  
J.G. Oghonyon ◽  
S.A. Okunuga ◽  
S.A. Bishop
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step ◽  
Predictor Corrector

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 A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
S. A. M. Yatim ◽  
Z. B. Ibrahim ◽  
K. I. Othman ◽  
M. B. Suleiman
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Computation Time ◽  
Quantitative Comparison ◽  
Initial Value ◽  
Step Size ◽  
Stiff Ordinary Differential Equations ◽  
Block Methods ◽  
Variable Step

We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF) for solving stiff initial value problems (IVPs). A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB's suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s.

scholarly journals A Dilated Trigonometrically Equipped Algorithm to Compute Periodic Vibrations through Block Milne’s Implementation

2018 ◽  
Vol 8 (4) ◽  
pp. 3126-3129
Author(s):  
J. G. Oghonyon ◽  
S. A. Bishop ◽  
K. S. Eke
Keyword(s):  
Error Control ◽  
Variable Step Size ◽  
Operational Mode ◽  
Convergence Criteria ◽  
Step Size ◽  
Variable Step ◽  
Predictor Corrector

This paper intends to investigate the use of a dilated trigonometrically equipped algorithm to compute periodic vibrations in block Milne's implementation. The block-Milne implementation is established by developing a block variable-step-size predictor-corrector method of Adam’s family using a dilated trigonometrically equipped algorithm. The execution is carried out using a block variable-step-size predictor-corrector method. This system has significant advantages that include the varying step-size and finding out the convergence-criteria and error control. Convergence-criteria and operational mode are discussed to showcase the accuracy and effectuality of the proposed approach.

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