Highly Accurate and Efficient Time Integration Methods with Unconditional Stability and Flexible Numerical Dissipation

This paper constructs highly accurate and efficient time integration methods for the solution of transient problems. The motion equations problems can be described by first-order ordinary differential equations, in which right-hand side is decomposed into two parts, a linear part nonlinear part. In proposed different orders, responses at previous step are transferred generalized Padé approximations, part’s approximated Gauss–Legendre quadrature together with explicit Runge–Kutta method, where method used to calculate function values points. For reducing computations rounding errors, 2m algorithm storing an incremental matrix employed calculation approximations. achieve higher-order accuracy, unconditional stability, flexible dissipation, zero-order overshoots. problems, accuracy reach 10−16 (computer precision), they enjoy advantages both efficiency compared some well-known methods, multi-step composite solving