A Numerical Integrator for Oscillatory Problems
Yusuf Dauda Jikantoro *
Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria.
Yahaya Badeggi Aliyu
Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria.
Aliyu Alhaji Ishaku Ma’ali
Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria.
Abdulkadir Abubakar
Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria.
Ismail Musa
Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Presented here is a numerical integrator, with sixth order of convergence, for solving oscillatory problems. Dispersion and dissipation errors are taken into account in the course of deriving the method. As a result, the method possesses dissipation of order infinity and dispersive of order six. Validity and effectiveness of the method are tested on a number of test problems. Results obtained show that the new method is better than its equals in the scientific literature.
Keywords: Dispersion, dissipation, oscillatory problems, differential equations, numerical experiment.