Block hybrid method using trigonometric basis for initial value problems with oscillating solutions

A continuous hybrid method using trigonometric basis (CHMTB) with one ‘off‐step’ point is developed and used to produce two discrete hybrid methods which are simultaneously applied as numerical integrators by assembling them into a block hybrid method with trigonometric basis (BHMTB) for solving oscillatory initial value problems (IVPs). The stability property of the BHMTB is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.