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Results tagged with jacobian
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Questions related to the calculation or use of the Jacobian matrix or its determinant. Not to be confused with the Jacobi iterative method for solving systems of linear equations. For those, use [iterative-method] instead.
3
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Is there a relatively simple way to extract the Jacobian from a Runge-Kutta 4/5 integrator?
So, if I framed this question properly, is it possible at some point during the RKF calculation to construct a Jacobian to pass out to Scipy along with the objective function evaluation? … As such, it does not require the solution of a nonlinear algebraic equation; Jacobian matrices are not required for that algorithm.
Is it possible to construct a Jacobian? …
- 30.4k
2
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Poisson-Nernst-Planck equations with ill-conditioned sparse matrix
If your Jacobian matrix is rank-deficient (as was the case in my problem, due to a nonconductive filler material in some cells), then direct methods will also have problems. … You should test your assembled Jacobian against a finite difference approximation for debugging purposes. …
- 30.4k
2
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Ill-conditioned Jacobian matrix from Nernst-Planck equation with Butler-Volmer reactions
algebraic equations, but it would behoove you to eliminate any algebraic equations if possible, since ODE solvers are generally faster than DAE solvers unless the DAE system has significantly sparser Jacobian … Will it help if I reorder the Jacobian matrix so that it is banded (currently the linear solver is LAPACK with dense matrix)? …
- 30.4k
2
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How to deal with complexity in numerical code, for example, when dealing with large Jacobian...
In addition to BrianBorcher's excellent suggestions, another possible approach for real-valued functions is to use the complex-step derivative approximation (see this article (paywalled) and this arti …
- 30.4k