1111[ ![ SciML Code Style] ( https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826 )] ( https://github.com/SciML/SciMLStyle )
1212
1313ModelingToolkit.jl is a modeling framework for high-performance symbolic-numeric computation
14- in scientific computing and scientific machine learning.
14+ in scientific computing and scientific machine learning.
1515It allows for users to give a high-level description of a model for
1616symbolic preprocessing to analyze and enhance the model. ModelingToolkit can
1717automatically generate fast functions for model components like Jacobians
@@ -71,7 +71,7 @@ plot(sol, idxs = (x, y))
7171
7272![ Lorenz2] ( https://user-images.githubusercontent.com/1814174/79118645-744eb580-7d5c-11ea-9c37-13c4efd585ca.png )
7373
74- This automatically will have generated fast Jacobian functions, making
74+ This will have automatically generated fast Jacobian functions, making
7575it more optimized than directly building a function. In addition, we can then
7676use ModelingToolkit to compose multiple ODE subsystems. Now, let's define two
7777interacting Lorenz equations and simulate the resulting Differential-Algebraic
@@ -81,7 +81,7 @@ Equation (DAE):
8181using ModelingToolkit
8282using ModelingToolkit: t_nounits as t, D_nounits as D
8383
84- # Defines two lorenz system model.s
84+ # Defines two lorenz system models.
8585eqs = [
8686 D (x) ~ σ * (y - x),
8787 D (y) ~ x * (ρ - z) - y,
@@ -124,7 +124,7 @@ plot(sol, idxs = (a, lorenz1.x, lorenz2.z))
124124
125125![ ] ( https://user-images.githubusercontent.com/17304743/187790221-528046c3-dbdb-4853-b977-799596c147f3.png )
126126
127- # Citation
127+ ## Citation
128128
129129If you use ModelingToolkit.jl in your research, please cite [ this paper] ( https://arxiv.org/abs/2103.05244 ) :
130130
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