scholarly journals Legendre wavelet solution of high order nonlinear ordinary delay differential equations

2019 ◽  
Vol 43 (3) ◽  
pp. 1339-1352 ◽  
Author(s):  
Sevin GÜMGÜM ◽  
Demet ERSOY ÖZDEK ◽  
Gökçe ÖZALTUN
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
High Order ◽  
Delay Differential

scholarly journals Word series high-order averaging of highly oscillatory differential equations with delay

2019 ◽  
Vol 4 (2) ◽  
pp. 445-454 ◽  
Author(s):  
J. M. Sanz-Serna ◽  
Beibei Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
High Order ◽  
Constant Delay ◽  
Integer Multiple ◽  
Averaged Equations ◽  
Highly Oscillatory ◽  
Highly Oscillatory Differential Equations ◽  
Delay Differential ◽  
Equations With Delay

AbstractWe show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.

Discrete Fourier Series Approximation to Periodic Solutions of Autonomous Delay Differential Equations

2005 ◽  
Author(s):  
David E. Gilsinn
Keyword(s):  
Fourier Series ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
High Order ◽  
Nonlinear Minimization ◽  
Fourier Series Approximation ◽  
Set Up ◽  
Delay Differential ◽  
Matrix Vector

This paper describes the algorithmic details involved in developing high-order Fourier series representations for periodic solutions to autonomous delay differential equations. Although the final approximate Fourier coefficients are computed by way of a nonlinear minimization algorithm, the steps to set up the objective function are shown to involve a sequence of matrix-vector operations. By proper coordination, these operations can be made very efficient so that high-order approximations can be obtained easily. An example of the calculations is shown for a Van der Pol equation with unit delay.

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