A nonlinear computational method for the solution of initial value problems for ordinary differential equations

2012 ◽  
Vol 47 (11) ◽  
pp. 17-22
Author(s):  
EA Ibijola ◽  
W. Sinkala
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Computational Method ◽  
Initial Value

scholarly journals A new computational algorithm for the solution of second order initial value problems in ordinary differential equations

2018 ◽  
Vol 3 (1) ◽  
pp. 167-174 ◽  
Author(s):  
P.K. Pandey
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Computational Algorithm ◽  
Second Order ◽  
Computational Method ◽  
Computationally Efficient ◽  
Initial Value ◽  
Computational Performance ◽  
Non Linear

AbstractIn this article, we propose a new computational method for second order initial value problems in ordinary differential equations. The algorithm developed is based on a local representation of theoretical solution of the second order initial value problem by a non-linear interpolating function. Numerical examples are solved to ensure the computational performance of the algorithm for both linear and non-linear initial value problems. From the results we obtained, the algorithm can be said computationally efficient and effective.

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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