scholarly journals Deriving numerical techniques with zero phase-lag and derivatives for initial value problems of second order

2012 ◽  
Author(s):  
D. F. Papadopoulos ◽  
O. T. Kosmas ◽  
T. E. Simos
Keyword(s):  
Initial Value Problems ◽  
Second Order ◽  
Phase Lag ◽  
Numerical Techniques ◽  
Initial Value ◽  
Zero Phase

scholarly journals Optimized Hybrid Methods for Solving Oscillatory Second Order Initial Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
N. Senu ◽  
F. Ismail ◽  
S. Z. Ahmad ◽  
M. Suleiman
Keyword(s):  
Hybrid Method ◽  
Initial Value Problems ◽  
Scientific Literature ◽  
Hybrid Methods ◽  
Second Order ◽  
Numerical Results ◽  
Phase Lag ◽  
Initial Value ◽  
Oscillatory Initial Value Problems

Two-step optimized hybrid methods of order five and order six are developed for the integration of second order oscillatory initial value problems. The optimized hybrid method (OHMs) are based on the existing nonzero dissipative hybrid methods. Phase-lag, dissipation or amplification error, and the differentiation of the phase-lag relations are required to obtain the methods. Phase-fitted methods based on the same nonzero dissipative hybrid methods are also constructed. Numerical results show that OHMs are more accurate compared to the phase-fitted methods and some well-known methods appeared in the scientific literature in solving oscillating second order initial value problems. It is also found that the nonzero dissipative hybrid methods are more suitable to be optimized than phase-fitted methods.

ON THE CONSTRUCTION OF EFFICIENT METHODS FOR SECOND ORDER IVPS WITH OSCILLATING SOLUTION

2001 ◽  
Vol 12 (10) ◽  
pp. 1453-1476 ◽  
Author(s):  
T. E. SIMOS ◽  
JESUS VIGO AGUIAR
Keyword(s):  
Initial Value Problems ◽  
Multistep Methods ◽  
Oscillating Solution ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
New Methods ◽  
Oscillating Solutions ◽  
Exponentially Fitted ◽  
Minimal Phase

In this paper we describe procedures for the construction of efficient methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions. Based on the described procedures we develop two simple and efficient multistep methods for the solution of the above problems. The first method is exponentially-fitted and trigonometrically-fitted and the second has a minimal phase-lag. Both methods are symmetric. Numerical results obtained for several well known problems show the efficiency of the new methods when they are compared with known methods in the literature.

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