Efficient Sixth Order P-Stable Methods with Minimal Local Truncation Error for $y"=f(x,y)$ (Journal of Computational Mathematics, 2002)
A family of symmetric (hybrid) two step sixth P-stable methods for the accurate numerical integration of second order periodic initial value problems have been considered in this paper. These methods, which require only three (new) function evaluation per iteration and per step integration. These methods have minimal local truncation error (LTE) and smaller phase-lag of sixth order than some sixth orders P-stable methods in [1-3,10-11]. The theoretical and numerical results show that these methods in this paper are more accurate and efficient than some methods proposed in [1-3,10].
Keywords: Second order periodic initial value problems; P-stable; Phase-lag; Local truncation error.