Time-Accurate and highly-Stable Explicit operators for stiff differential equations

Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle physical terms implicitly is proposed. Both and numerical stiffness originating from convection, diffusion source (typically related reaction) can be handled by set of predefined Time-Accurate highly-Stable Explicit (TASE) operators unified framework. The proposed TASE act as preconditioners on the deployed any existing explicit straightforwardly. resulting time integration remain original schemes, yet with nearly unconditional stability. designed arbitrarily high-order accurate Richardson extrapolation such that accuracy order method preserved. Theoretical analyses stability diagrams show s-stages sth-order Runge-Kutta (RK) unconditionally when preconditioned p?s p?2. On other hand, RK p>2 stable. only free parameter determined priori based arguments. Unlike classical methods, methodology allows for non-linear problems arbitrary without requiring nonlinear system equations. A benchmark strong simulated assess performance method. Numerical results suggest preserves very-large steps all considered cases. As an alternative established strategies, promising efficient computation problems.