All Questions
9 questions
1
vote
1
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359
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Fitting delay differential equations (DDE)
I have the following differential equations:
$$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(t)}{6.19} \Big)- \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = c (1 - B(t)) - d B(t) S(t) - 3 c (1 - B(t - 18)),$$
where $B(t -...
user95418
1
vote
0
answers
472
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How to include impulses in differential equations?
I have two coupled differential equations as follows:
$$S'(t) = - \frac{a}{1 + B(t)} S(t),$$
$$B'(t) = \frac{c}{1 + S(t)} B(t) (1 - B(t)) - d B^2(t) \Big( \frac{1 - B(t)}{B(t)} \Big)^n,$$
where $a$, $...
user95418
0
votes
1
answer
214
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Using ParametricNDSolveValue and MultiNonlinearModelFit to fit an ODE system to datasets
I asked a question here about fitting an ODE system to given datasets. The great answer of @ydd solved the problem nicely. In the mentioned answer, the initial values are taken as the initial points ...
user95418
4
votes
2
answers
447
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Modeling experimental data with differential equations
I have the following two sets of experimental data, which show the dependencies of two quantities, namely, $S$ and $B$, on time ($0$ h, $3$ h, $6$ h, $9$ h, $15$ h, $18$ h, $21$ h, and $24$ h):
...
user95418
2
votes
2
answers
455
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Fitting Asymptotic Ansatz to Numerical solution of Differential equation
Consider the following differential equation: $$ \frac{1}{a} \frac{dy}{dx} = -\frac{1}{y} e^{-\frac{1}{y}} $$ with initial condition $y(0) = 1$ and $a = 10$. This is easily solved numerically with $...
- 779
10
votes
2
answers
1k
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Fitting experimental data by using ParametricNDSolveValue and NonlinearModelFit
I am a newcomer to Mathematica.
Basically I just want to fit the data (enzyme kinetic data) shown below to a system of odes' by using NonlinearModelFit. The data, an 101x2 array, contains time in the ...
- 101
1
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1
answer
172
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Paramter Scans and $\chi^2$ Test in Mathematica
Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$?
...
- 950
0
votes
1
answer
234
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How to adjust excel data for NonlinearModelFit?
I'm really new to Mathematica and I'm facing a problem and would really appreciate some help! Maybe my question is similar to one described in How to fit 3 data sets to a model of 4 differential ...
- 21
33
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2
answers
8k
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How to fit 3 data sets to a model of 4 differential equations?
I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
- 333