scholarly journals Parallel algorithms for the solving both of non-linear systems and initial-value problems for systems of ordinary differential equations on multi-core computers with processors Intel Xeon Phi

2018 ◽  
pp. 054-060
Author(s):  
T.O. Gerasimova ◽  
◽  
A.N. Nesterenko ◽  
Keyword(s):  
Differential Equations ◽  
Parallel Algorithms ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Initial Value Problems ◽  
Xeon Phi ◽  
Intel Xeon Phi ◽  
Initial Value ◽  
Non Linear ◽  
Non Linear Systems

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 stability test for non linear systems of ordinary differential equations based on the Gershgorin circles

2018 ◽  
Vol 11 (91) ◽  
pp. 4541-4548 ◽  
Author(s):  
Danilo Alonso Ortega Bejarano ◽  
Eduardo Ibarguen-Mondragon ◽  
Enith Amanda Gomez-Hernandez
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Stability Test ◽  
Non Linear ◽  
Non Linear Systems

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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