# Tagged Questions

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### reducing an n-order differential equation to a first order system of equations using either sagemath or sympy

I want to reduce a n-order ordinary differential equation into a first order system of equations. This is in preparation for numerical analysis. I use both Sympy and Sagemath for Computer Algebra, but ...
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### Explicit probability conserving solvers for Pauli equation?

I know that there exist probability conserving explicit solvers for time-dependent SchrÃ¶dinger's equation, for example, Visscher's one. But when I tried to add spin into account in this scheme, it ...
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### Delay Differential Equations Numerical methods

I have a general question about delay differential equations. I know that even simple ones hardly have analytic solutions and mine clearly doesn't have any as it is a system of non-linear delay ...
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### Local positivity of solutions to linear differential inequalities (Chaplygin's theorem)

According to the entry "Differential inequality" of the Encyclopedia of Mathematics http://www.encyclopediaofmath.org/index.php/Differential_inequality the following result is due to Chaplygin ...
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### Random, Linear, Homogeneous Difference Equations and Time Integration Methods for ODEs

Most methods (that I know of) of numerically approximating the solution of ODEs are "general linear methods". For this type of method, the so-called 'linear stability' is examined by applying the ...
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### What is state of the art for the Shooting Method?

I am interested in examples where the Shooting Method has been used to find solutions to systems of ordinary differential equations that are either reasonably large systems, or the search ...
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### Adaptive controllers for stiff ODE and DAE integrators

I'm looking for adaptive controllers (adaptive in both step size and order) for stiff integrators. I have asymptotically correct error estimates for the current method and all candidate methods of ...
I am trying to optimize a function of the following form: $L = \int_{t=0}^{T}(AR-x)dt$, where A is a system parameter i.e. I am trying to find the optimum x(t) that minimizes L over all admissible ...