Functional‐preserving predictor‐corrector multiderivative schemes

Abstract In this work, we develop a class of high‐order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite‐Birkhoff‐Predictor‐Corrector (HBPC) and technique relaxation for numerical ordinary differential equations (ODEs). We explain algorithm in detail show results two‐ three‐derivative methods, comparing relaxed unrelaxed methods. The demonstrate that, at slight cost relaxation, an improved scheme obtained.