Jacobian matrix in ode15s
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Hi everyone,
I am using ode15s to solve a set of stiff odes and the final model is developed in the form of
where M(t,y) is the mass matrix, and y is the generalised coordinate vector. According to the syntax of ode15s, it is crucial to provide its Jacobian matrix to raise the accuracy.
I do not know too much numerical calculation of stiff odes, and here I want to know, is the Jacobian matrix JJ calculated in this manner:
If not, how to arrive at a correct one?
Many thanks!
3 个评论
Torsten
about 4 hours 前
编辑:Torsten
about 4 hours 前
BTW, are there any ways to format a good odeset to raise the computational efficiency and accuracy?
RelTol and AbsTol are the usual parameters that influence accuracy. I doubt there will be a great gain in efficiency by supplying the Jacobian matrix - especially since most probably you had to use finite differencing like ode15s itself because of the complexity of your model.
I'd start with the standard settings for odeset - often, beginners have good intentions, but tend to make things worse.
回答(1 个)
Dheeraj
about 13 hours 前
Hi Tony chegg,
I understand you want to know how to calculate jacobian matrix in order to increase the accuracy of your model.
When solving stiff differential equations with "ODE15s", you are typically dealing with equations of the form:
where is the mass matrix, and represents the nonlinear term.
To use "ODE15s" effectively, you need to provide the Jacobian matrix of the function with respect to y, which is used to handle the stiffness in the system. This Jacobian matrix is denoted as "J" and is defined as:
You can easily calculate Jacobian matrix if you have an explicit expression for, you can compute the Jacobian matrix analytically. This involves differentiating with respect to each component of y.
Or You could use "jacobian" fucntion part of Symbolic Math Toolbox to do the same.
You could refer to the below MATLAB's documentation to know more about "jacobian" fucntion and it's usage:
Thank You.
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