@ARTICLE{Riahi2022225,
	author = {Riahi, Mohamed Kamel},
	title = {PiTSBiCG: Parallel in time Stable Bi-Conjugate gradient algorithm},
	year = {2022},
	journal = {Applied Numerical Mathematics},
	volume = {181},
	pages = {225-233},
	doi = {10.1016/j.apnum.2022.06.004},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85132505838&doi=10.1016%2fj.apnum.2022.06.004&partnerID=40&md5=5e9a3a3aae488c543249836121b90d4c},
author_keywords={Parallel in time algorithm, BiCGStab, parareal, Acceleration, Parallel computing,
Numerical Simulation of PDEs},document_type={Article},
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) has great potential in 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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