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 Direct Two-Point Block One-Step Method for Solving General Second-Order Ordinary Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zanariah Abdul Majid ◽  
Nur Zahidah Mokhtar ◽  
Mohamed Suleiman
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multistep Method ◽  
Second Order ◽  
Variable Step Size ◽  
Step Size ◽  
Step Method ◽  
One Step ◽  
The Stability ◽  
The One

A direct two-point block one-step method for solving general second-order ordinary differential equations (ODEs) directly is presented in this paper. The one-step block method will solve the second-order ODEs without reducing to first-order equations. The direct solutions of the general second-order ODEs will be calculated at two points simultaneously using variable step size. The method is formulated using the linear multistep method, but the new method possesses the desirable feature of the one-step method. The implementation is based on the predictor and corrector formulas in thePE(CE)mmode. The stability and precision of this method will also be analyzed and deliberated. Numerical results are given to show the efficiency of the proposed method and will be compared with the existing method.

scholarly journals Half Step Numerical Method for Solution of Second Order Initial Value Problems

2021 ◽  
pp. 77-81
Author(s):  
Adeniran Adebayo O. ◽  
Edaogbogun Kikelomo
Keyword(s):  
Numerical Method ◽  
Initial Value Problems ◽  
Second Order ◽  
Variable Step Size ◽  
Initial Value ◽  
Step Size ◽  
Stable Order ◽  
Variable Step ◽  
Interpolation Technique ◽  
Order Four

This paper presents a half step numerical method for solving directly general second order initial value problems. The scheme is developed via collocation and interpolation technique invoked on power series polynomial. The proposed method is consistent, zero stable, order four and three. This method can estimate the approximate solution at both step and off step points simultaneously by using variable step size. Numerical results are given to show the efficiency of the proposed scheme over some existing schemes of same and higher order.

An efficient variable step-size rational Falkner-type method for solving the special second-order IVP

2016 ◽  
Vol 291 ◽  
pp. 39-51 ◽  
Author(s):  
Higinio Ramos ◽  
Gurjinder Singh ◽  
V. Kanwar ◽  
Saurabh Bhatia
Keyword(s):  
Second Order ◽  
Variable Step Size ◽  
Step Size ◽  
Type Method ◽  
Variable Step
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