High Order Symmetric Super-Implicit Hybrid LMMs with Minimal Phase-Lag. Solving differential equations using the numerically stable Super-Implicit Hybrid formula

      Аннотация: Ordinary differential equations arises in the modelling of physical phenomenon in sciences and beyond. Some of these physical phenomenon cannot be solved analytically, this is why accurate and efficient numerical integration process is essential. This study focuses on the construction of a unique Super-Implicit linear multi-step methods with minimal phase-lag error constant. The proposed p-stable methods were achieved through the introduction of hybrid approach in order to circumvent the famous order barrier impose on linear multi-step methods. The numerical experiments presented in this work are facts to prove beyond any reasonable doubt that the newly developed method is not only suitable for the solution of an orbital problem but capable of solving stiff-oscillatory problems even when compared with existing results.

Ключевые слова: Differential Equations, Periodicity, symmetric, Super-Implicit, Hybrid LMMs, Phase-Lag