On the construction of a type of composite time integration methods

The paper provides the general construction principles of a type of composite time integration methods combining the trapezoidal rule (TR) and the backward differential formula (BDF) by discussing the effects of designable parameters on the properties of composite methods. The designable parameters include the number of sub-steps, the number of time difference points used in BDF and the methods used in sub-steps. Through respective changing these parameters, a series of novel composite time integration methods, such as T(2–5)BDF3 and OT3BDF4 and OTBDF3BDF methods etc., are constructed. It follows that increasing both the number of sub-steps and the number of time difference points can improve the low-frequency accuracy, and the composite methods with similar properties can be developed by using the same parameter optimization rules even though different methods are used in sub-steps. Linear and nonlinear numerical experiments are conducted to check the properties of the proposed methods through comparing with some of the existing composite time integration methods and validate the conclusions.