In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the nonlinear CH equation. We use diagonalization technique on all-at-once system to develop efficient iterative time parallel methods for investigating the solution behaviour of said equations. We present the convergence analysis of Parallel-in-Time (PinT) algorithms. We verify our findings by presenting numerical results.

翻译：本文设计、分析并实现了一类四阶时间依赖偏微分方程（PDEs）的高效时间并行方法，这类方程包括双调和热方程、线性化Cahn-Hilliard (CH)方程以及非线性CH方程。我们采用一次性系统的对角化技术，开发了高效的迭代式时间并行方法，用于研究上述方程的解行为。我们给出了时空并行（PinT）算法的收敛性分析，并通过数值结果验证了我们的结论。