General issues that arise in the context of second- and higher-order time-discretizations of multi-material problems by multi-step schemes are highlighted, and solutions to these issues are presented in the form of redesigned implicit time-integrators.
The backward difference formula (BDF) class of multi-step schemes has been widely used as time integration method for both ordinary and partial differential equations, see [19 27].
Convection terms are explicitly handled using a second-order multi-step scheme.
A multi-step scheme of the algorithm is presented and applied to the blank design of sheet metal parts.
A series of 1,3-dipolar cycloaddition products of functionalized nitrones with 1,3-propene sultone and maleimide was synthesized through a multi-step scheme.
Although there were 100 base steps, PKDGRAV3 uses a multi-stepping scheme where particles choose their own time-step rung based on the time-step criterion discussed previously.
In this paper, we extend the "Fingerprinting method", a method that can be used to determine the relative specificities that an enzyme has for the various reactions that it can catalyze in a multi-step reaction scheme, to reaction schemes involving processive action.
However, recovery of polypeptides from recombinant protein expression systems typically involves multi-step purification schemes.
Multi-step reaction schemes utilizing various genetic engineering techniques described above were employed for solid-phase gene assembly.
(i) The multi-step iterative scheme (3.1) of [13] is extended to develop our relaxed extragradient iterative scheme (3.1) by virtue of Korpelevich's extragradient method and the strongly positive bounded linear operator approach.
(i) The multi-step iterative scheme (3.1) of [43] is extended to develop a hybrid extragradient viscosity iterative scheme (3.1) by virtue of Korpelevich's extragradient method, hybrid steepest-descent method [40] and gradient-projection method (GPM) with regularization.
