Solving oscillatory problems using a block hybrid trigonometrically fitted method with two off-step points

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