# Questions tagged [differentiation]

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### second order finite function for 2D function in Python

My task is to Implement the derivative with the 2nd order finite difference for 2D functions. Evaluate the accuracy of the numerical derivatives of J(x,y) at the point (x = 5, y = −2) by determining ...
3answers
181 views

### Calculating the antiderivative numerically

HeIIo everybody, in the standard literature topics like numerical differentiation and numerical integration are usually discussed in detail. However, numerical integration is not the same as ...
0answers
88 views

### How to derive the adjoint sensitivity equations for a least squares objective function gradient

The Problem I would like to determine the gradient of a least squares objective function which depends on a vector of 40 parameters $p$, and the solution of a system of 32 differential equations. In ...
2answers
5k views

### Solving coupled differential equations in Python, 2nd order

I have a system of coupled differential equations, one of which is second-order. I am looking for a way to solve them in Python. I would be extremely grateful for any advice on how can I do that! $k$...
1answer
99 views

### Finding derivative of Matrix at different grid points using Finite difference methods/ Cholesky Factorization

I want to code this problem in MATLAB. It would be a huge help if someone can suggest to me how I can approach it. I need to solve the below-highlighted equation, I need ...
4answers
880 views

### Example where autodiff works but symbolic differentiation will not?

According to the survey paper on autodiff (linked) Autodiff works on inputs that cannot be specified in closed form but can be described by a sequence of code, each component of which is ...
0answers
79 views

### How to get the derivatives of the determinant and inverse of 2nd-order tensor wrt itself in SymPy?

I have a second-order tensor for which I need to compute the derivatives of its determinant and inverse w.r.t. itself. The equations are as follows: \frac{\partial \, det(\mathbf{F})}{\partial F_{...