A comparison of some ODE solvers which require Jacobian evaluations

Day, J.D.; Murthy, D. N. P.

doi:10.1016/0377-0427(83)90014-6

Cited by 6 publications

(3 citation statements)

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“…Although, implicit solvers are computationally more expensive as they generate a Jacobian matrix and solve a set of algebraic equations at every time step using a Newton-like method. To reduce such extra cost, the implicit solver offers a Solver Jacobian method that allows improving the simulation performance of the implicit solvers [44]. Stiff differential equations are numerically unstable unless the step size is extremely small.…”

Section: Numerical Solutionmentioning

confidence: 99%

Phenomenological kinetic model of the nano-bainitic steels to characterize the dynamics of the autocatalytic nucleation process

2020

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A kinetic model has been proposed in the present work, which formulates the dynamic nature of autocatalysis. The autocatalytic factor is quantified in the present work which involves interaction energy between bainite nucleus and stress field generated by existing bainite. This interaction energy provides the stored energy for autocatalytic nucleation and eventually reduces the nucleation barrier of bainite transformation. The change in Gibbs free energy due to carbon partitioning will also alter the autocatalytic nucleation with the bainite transformation. The model also evaluates the activation energy due to dislocation barrier, which is arising by solid solution strengthening of austenite. The slow kinetics at low transformation temperature is due to the larger activation energy of the dislocation barrier, which provides greater resistance to atomic displacement during transformation. The interaction energy between bainite nucleus and stress field generated by existing bainite was validated by determining the transformation shear strain exhibited in austenite which was found to be in the range as reported in the literature for displacive transformations.

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Section: Numerical Solutionmentioning

confidence: 99%

Phenomenological kinetic model of the nano-bainitic steels to characterize the dynamics of the autocatalytic nucleation process

2020

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“…If we seek a method of the form (2.2) such that P2,, and f12,, are unchanged from the minimum configuration (4,2,4) process, then the consistency equations for a (3, 2,4) 3(4,2,4) process of the form (1.2) which is the Lstable.…”

Section: The 3(424) Processmentioning

confidence: 99%

“…The methods were tested with some equations taken from reference [4]. The equations used were: The calculated solution was required to satisfy an absolute error tolerance of lo-^?…”

Section: Numerical Testingmentioning

confidence: 99%