scholarly journals Adam’s block with first and second derivative future points for initial value problems in ordinary differential equations

2021 ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Second Derivative ◽  
Initial Value

scholarly journals A Family of Stiffly Stable Second Derivative Block Methods for Initial Value Problems in Ordinary Differential Equations

2019 ◽  
pp. 221-239 ◽  
Author(s):  
Samuel A. Ajayi ◽  
Kingsley O. Muka ◽  
Oluwasegun M. Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Absolute Stability ◽  
Truncation Error ◽  
Second Derivative ◽  
Initial Value ◽  
First Order ◽  
Stiff Ordinary Differential Equations ◽  
Block Methods

In this paper, we present a family of stiffly stable second derivative block methods (SDBMs) suitable for solving first-order stiff ordinary differential equations (ODEs). The methods proposed herein are consistent and zero stable, hence, they are convergent. Furthermore, we investigate the local truncation error and the region of absolute stability of the SDBMs. A flowchart, describing this procedure is illustrated. Some of the developed schemes are shown to be A-stable and L-stable, while some are found to be A()-stable. The numerical results show that our SDBMs are stiffly stable and give better approximations than the existing methods in the literature.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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