Revised trigonometrically fitted two-step hybrid methods with equation dependent coefficients for highly oscillatory problems

For the numerical integration of highly oscillatory problems, revised trigonometrically fitted two-step hybrid methods (RTFTSH) with equation dependent coefficients are considered. The local truncation errors, stability and phase properties of the new method are analyzed. A feature of the new type of the methods is that the errors in the internal stages are assumed to contribute to the accuracy of the update. A new revised method RTFTSH4 of algebraic order four and phase-lag order four is derived. Numerical experiments are reported to show that the new method RTFTSH4 is much more efficient and robust than the standard fourth order method STFTSH4. (C) 2016 Published by Elsevier B.V.