A new numerical method for the integration of highly oscillatory second-order ordinary differential equations

• Published in: Applied numerical mathematics Vol. 13; no. 1; pp. 57 - 67
• Main Author: Denk, G.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.1993; Elsevier
• Subjects: absolute stability; consistency; convergence; Exact sciences and technology; Mathematics; multistep method; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; oscillatory solutions; Sciences and techniques of general use; oscillatory solutions; Ordinary differential equations; multistep method; absolute stability; convergence; consistency; Second order equation; Multistep method; Oscillatory solution; Differential equation; Absolute stability; Numerical convergence; Discretization method
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/0168-9274(93)90131-A

This paper presents a new discretization scheme for the efficient integration of highly oscillatory second-order ordinary differential equations. The discretization scheme is based on the principle of coherence proposed by Hersch. The analysis of the formulas reveals properties such as absolute stability and P-stability which indicate the ability of the method to handle highly oscillatory differential equations. This is confirmed by numerical results.