Functional‐preserving predictor‐corrector multiderivative schemes

Abstract

AbstractIn 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) methods and the technique of relaxation for numerical methods of ordinary differential equations (ODEs). We explain the algorithm in detail and show numerical results for two‐ and three‐derivative methods, comparing relaxed and unrelaxed methods. The numerical results demonstrate that, at the slight cost of the relaxation, an improved scheme is obtained.