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Implicit time stepping typically requires solution of one or several linear systems with a matrix I-τJ per time step where J is the Jacobian matrix. If solution of these systems is expensive, replacing I-τJ with its approximate matrix factorization (AMF) (I-τR)(I-τV), R+V=J, often leads to a good compromise between stability and accuracy of the time integration on the one hand and its efficiency on...
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