# Questions tagged [jacobian]

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.

44 questions
Filter by
Sorted by
Tagged with
30 views

### Can't understand the proof of the Time-Rescaling theorem

I was reading the following paper: The time-rescaling theorem and its application to neural spike train data analysis and I have some difficulties understanding the proof of the time-rescaling-theorem,...
103 views

### How do I calculate the Jacobian of this function?

I have two vectors $r$ and $m$. Both vectors are $N\times1$. A function is calculated as - $F(1:N) = \phi r + (r^3 + rm^2)$ $F(N+1:2N) = \phi m + (m^3+mr^2)$ ...
87 views

### Calculating the Jacobian for a function containing a derivative

I have the equation $F(t) = \phi u + \frac{1}{2}\frac{d^2u}{dt^2} + u^3$ and broadly speaking, my task is to calculate the $\phi$ and $u(t)$ such that $F(t) = 0$. I am testing out a new algorithm to ...
536 views

### Specifying ode solver options to speed up compute time

I'm specifying the 'JPattern', sparsity_pattern in the ode options to speed up the compute time of my actual system. I am sharing a sample code below to show how I ...
52 views

### Jacobian matrix cutoff in ODE solver

I am studying an implementation of a semi-implicit Runge Kutta method of 3. order (SIRK3) from the book by Villadsen & Michelsen (1978), Solution of differential equation models by polynomial ...
197 views

### How to verify solution to pre-conditioned linear systems solver?

I am solving Ax=b. A has a very large condition number (> O(10^10)) I am using the conjugate gradients method with point jacobi pre-conditioning. I obtained a solution 'x' that "looks" reasonable. ...
67 views

### Solving differential equation by specifying jacobian pattern

This is a follow up to my previous question posted here I'm trying to construct the sparsity pattern of the jacobian matrix to speed up the computation of a large system of odes. The following is the ...
48 views

### solving differential equations with jacobian pattern

I'm trying to compare the simulation time for solving a system of differential equations with and without jacobian pattern for a toy model using ode15s in MATLAB. ...
34 views

### Estimating the Jacobian in Harmonic Balance Method

I am trying to solve a set of ODEs using the Harmonic Balance method. In order to do this, I need to compute the Jacobian of the set of equations. However I am very confused regarding the dimensions ...
43 views

...
108 views

### Method of Lines: How to simplify Jacobian with periodic BCs?

Consider the advection equation $$\frac{\partial u}{\partial t}+c(x)\frac{\partial u}{\partial x}=0.$$ With periodic boundary condtitions in $x$ with period $L$, i.e. $u(x,t)=u(x+L,t)$ and initial ...