High-order implicit time integration scheme based on Padé expansions

A single-step high-order implicit time integration scheme for the solution of transient and wave propagation problems is presented. It constructed from Pad\'e expansions matrix exponential a system first-order ordinary differential equations formulated in state-space. computationally efficient developed exploiting techniques polynomial factorization partial fractions rational functions, by decoupling displacement velocity vectors. An important feature novel algorithm that no direct inversion mass required. From diagonal expansion order $M$ time-stepping $2M$ developed. Here, each elevation accuracy two orders results an additional real or complex sparse to be solved. These systems are comparable complexity standard Newmark method, i.e., effective linear combination static stiffness, damping, matrices. shown second-order equivalent Newmark's constant average acceleration often also referred as trapezoidal rule. The proposed integrator has been implemented MATLAB using built-in equation solvers. In this article, numerical examples featuring nearly one million degrees freedom High-accuracy efficiency comparison with common schemes observed. MATLAB-implementation available authors upon request GitHub repository (to added).