Explicit eighth order methods for the numerical integration of initial-value problems with periodic or oscillating solutions

1999 ◽  
Vol 119 (1) ◽  
pp. 32-44 ◽  
Author(s):  
T.E. Simos
Keyword(s):  
Numerical Integration ◽  
Initial Value Problems ◽  
Initial Value ◽  
Eighth Order ◽  
Oscillating Solutions

EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs

2008 ◽  
Vol 19 (06) ◽  
pp. 957-970 ◽  
Author(s):  
I. Th. FAMELIS
Keyword(s):  
Initial Value Problems ◽  
Computational Cost ◽  
Phase Lag ◽  
Initial Value ◽  
Eighth Order ◽  
Oscillatory Solutions ◽  
Numerical Tests ◽  
New Methods ◽  
Oscillating Solutions ◽  
Algebraic Order

Using a new methodology for deriving hybrid Numerov-type schemes, we present new explicit methods for the solution of second order initial value problems with oscillating solutions. The new methods attain algebraic order eight at a cost of eight function evaluations per step which is the most economical in computational cost that can be found in the literature. The methods have high amplification and phase-lag order characteristics in order to suit to the solution of problems with oscillatory solutions. The numerical tests in a variety of problems justify our effort.

A Zero Dispersion RKN Method for the Numerical Integration of Initial Value Problems with Oscillating Solutions

2009 ◽  
Author(s):  
D. F. Papadopoulos ◽  
Z. A. Anastassi ◽  
T. E. Simos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Numerical Integration ◽  
Initial Value Problems ◽  
Initial Value ◽  
Oscillating Solutions

scholarly journals On the numerical integration of second-order initial value problems with a periodic forcing function

Computing ◽  
1986 ◽  
Vol 37 (3) ◽  
pp. 195-218 ◽  
Author(s):  
P. J. van der Houwen ◽  
B. P. Sommeijer ◽  
K. Strehmel ◽  
R. Weiner
Keyword(s):  
Numerical Integration ◽  
Initial Value Problems ◽  
Second Order ◽  
Periodic Forcing ◽  
Initial Value ◽  
Forcing Function
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