scholarly journals Step Change Strategies for Multistep Methods

1985 ◽  
Vol 14 (196) ◽  
Author(s):  
Ole Østerby
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multistep Methods ◽  
Step Change ◽  
Change Strategies ◽  
Step Size ◽  
Step Method ◽  
Adams Methods

When a system of ordinary differential equations is solved using a step-by-step method it is often desirable to change the step size during the course of the integration. We show that the commonly used formulas for calculating the new step sizes are not correct for multistep methods and we derive correct formulas for Adams methods.

scholarly journals NUMERICAL SOLUTION FOR SOLVING SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS USING BLOCK METHOD

2012 ◽  
Vol 09 ◽  
pp. 560-565 ◽  
Author(s):  
NUR ZAHIDAH MUKHTAR ◽  
ZANARIAH ABDUL MAJID ◽  
FUDZIAH ISMAIL ◽  
MOHAMED SULEIMAN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fluid Dynamic ◽  
Electric Circuit ◽  
Second Order ◽  
Variable Step Size ◽  
Step Size ◽  
Step Method ◽  
Mathematical Problems ◽  
One Step

The purpose of this paper is to present a four point direct block one-step method for solving directly the general second order nonstiff initial value problems (IVPs) of ordinary differential equations (ODEs). The mathematical problems in real world can be written in the form of differential equations and arise in the fields of science and engineering such as fluid dynamic, electric circuit, motion of rocket or satellite and other area of application. The proposed method will estimate the approximation solutions at four points simultaneously by using variable step size. Numerical results are given to show the efficiency of the proposed method.

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.

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