Abstract
AbstractA functionally-fitted Numerov-type method is developed for the numerical solution of second-order initial-value problems with oscillatory solutions. The basis functions are considered among trigonometric and hyperbolic ones. The characteristics of the method are studied, particularly, it is shown that it has a third order of convergence for the general second-order ordinary differential equation, $$y''=f \left( x,y,y' \right) $$
y
′
′
=
f
x
,
y
,
y
′
, it is a fourth order convergent method for the special second-order ordinary differential equation, $$y''=f \left( x,y\right) $$
y
′
′
=
f
x
,
y
. Comparison with other methods in the literature, even of higher order, shows the good performance of the proposed method.
Publisher
Springer Science and Business Media LLC
Reference49 articles.
1. Abdulganiy, R.I., Akinfenwa, O.A., Okunuga, S.A.: Maximal order block trigonometrically fitted scheme for the numerical treatment of second order initial value problem with oscillating solutions. Int. J. Math. Anal. Optim. 2017, 168–186 (2018)
2. Andersen, C.M., Geer, J.F.: Power series expansions for the frequency and period of the limit cycle of the Van Der Pol equation. SIAM J. Appl. Math. 42(3), 678–693 (1982)
3. Archar, S.D.: Symmetric multistep Obrechkoff methods with zero phase-lag for periodic initial value problems of second order differential equations. J. Appl. Math. Comput. 218, 2237–2248 (2011)
4. Awoyemi, D.O.: A P-stable linear multistep method for solving general third order ordinary differential equations. Int. J. Comput. Math. 80(8), 987–993 (2003)
5. Brugnano, L., Trigiante, D.: Solving Differential Problems by Multistep Initial and Boundary Value Methods. Gordan and Breach, Amsterdam (1998)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献