# Questions tagged [differential-equations]

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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### How to solve the tsunami model and animate the shallow water wave?

Backslide introduced in 9.0, persisting through 11.3. Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation. How to ...
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### Transcritical Bifurcation phase portraits

An example equation for a Transcritical Bifurcations is given by: $$\dfrac{dx}{dt} = f(x, r) = r x - x^2$$ In Mathematica, we can define the function as: ...
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### Plotting a Bifurcation diagram

I have the following system equation v'(t)=2*G*J1[v(t-τ)]cos(w*τ)-v(t) How do you plot the bifurcation diagram, τ in the x ...
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### Calculating a potential function using the finite element method

This is my first attempt to use the Finite Element method available in version 10. There are questions and I am very open to suggestions. My example is flow around a cylinder which is a well known ...
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### NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
2answers
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### Getting rid of spikes in the PDE solution

Bug introduced in 10.0 and fixed in 10.3 Note: In 10.0, Rationalize[fd, 0] was needed or mesh generation would fail. Preamble: I am solving a PDE in a domain ...
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### Speed up NDSolve compared to Python (calls to LSODA)

I migrated a numerical model code from Python to Mathematica and am surprised how much faster the Python version runs. Profiling of the Python version tells me that it is about 100 times faster (120 ...
4answers
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### 3D FEM Vector Potential

I am trying to reproduce an FEM result in a paper. Due to possible copyright I cannot show the result directly but fortunately there is a free link An Incomplete Gauge for 3D Nodal Finite Element ...
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### Reveal the formal PDE of FiniteElement

When FiniteElement method is used, the differential equations will first be transformed to certain standard form (named as formal PDE in recent FEM document), and ...
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### Calculating the error in the solution of a system of ODEs

I have solved system of ODEs by using NDSolve. I want to calculate the error of the solutions. So far I have calculated error by plotting results of each equation. ...