Abstract
This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating the parallel in time problem algebraically and solve it using an adapted Bi-Conjugate gradient stabilized method. The proposed Parallel in time Stable Bi-Conjugate algorithm (PiTSBiCG for short) has a great potential to stabilizing the parallel resolution for a variety of problems. In this work, we describe the mathematical approach to the new algorithm and provide numerical evidence that shows its superiority to the standard parareal method.
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