A two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-value problem

1991 ◽  
Vol 39 (1-2) ◽  
pp. 135-140 ◽  
Author(s):  
T. E. Simos
Keyword(s):  
Numerical Integration ◽  
Initial Value Problem ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
Step Method

EXPLICIT EIGHTH ORDER TWO-STEP METHODS WITH NINE STAGES FOR INTEGRATING OSCILLATORY PROBLEMS

2006 ◽  
Vol 17 (06) ◽  
pp. 861-876 ◽  
Author(s):  
Ch. TSITOURAS
Keyword(s):  
Initial Value Problem ◽  
Second Order ◽  
Initial Value ◽  
Step Method ◽  
Eighth Order ◽  
Oscillatory Solutions ◽  
Numerical Tests ◽  
Phase Errors ◽  
Matlab Program ◽  
Algebraic Order

We present a new explicit hybrid two step method for the solution of second order initial value problem. It costs only nine function evaluations per step and attains eighth algebraic order so it is the cheapest in the literature. Its coefficients are chosen to reduce amplification and phase errors. Thus the method is well suited for facing problems with oscillatory solutions. After implementing a MATLAB program, we proceed with numerical tests that justify our effort.

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