# Tagged Questions

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

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### Partial differential equation with infinity limit

How do I get Mathematica to solve the following partial differential equation $$\frac{\partial u(y,t)}{\partial t} = \nu \frac{\partial^2 u(y,t)}{\partial y^2}+\frac{\partial U_0(t)}{\partial t}$$ ...
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### Reaction-diffusion PDE with NDSolve: either very slow or very inaccurate

I am struggling to have Mathematica 10.3 solve a system of PDE's (with periodic boundary conditions and random initial conditions), but either it produces a set of very noisy InterpolatingFunction ...
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### Solve and plot differential equation

I want to solve this differential equation $\qquad y'(x)=\frac{x-y(x)}{1-y(x)-x}$ and plot it's solution. But DSolve doesn's work. ...
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### NDeigensystem returns error due to mesh discretization when calculating vibrations of a cantilever

There was an transcription error in the code I provided in a previous post: NDeigensystem returns complex non-hermitian error for the calculation of vibrations of a cantilever This resulted in it ...
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### WhenEvent and Resetting of Variable in PDE when operation succeeds [closed]

I have had success in using WhenEvent to reset or change a variable within NDSolve with ordinary differential equations. My ...
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### Fourier-style solutions to differential equations, not piecewise polynomials

NDSolve returns piecewise polynomials. Is there any way I can get a single (non piecewise) function consisting of sines and cosines instead? Sort of a "Fourier approximation" to the solution of my ...
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### Changing from Cartesian to polar coordinates in partial differential equation [duplicate]

I have a partial differential equation: $$\left(x^2+y^2\right)\frac{{{\partial ^2}u(x,y)}}{{\partial {x^2}}} + x^2\frac{{{\partial ^2}u(x,y)}}{{\partial {y^2}}}=0$$ How to change from Cartesian to ...
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### System of equations is solved by NDSolve over just a tiny domain

I'm solving numerically a system of differential equations with the use of NDSolve. The numerical integration works only a very small interval of the argument. I'm ...
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### Issue plotting PDE solution with manipulate

I am trying to plot the solution to the following PDE with the help of mathematica, however, when trying to employ manipulate to animate the behavior, I find that if I try this: ...
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### Numerical instabilities of a convection-(non-)diffusion equation when shrinking from a square to a triangular domain

I am trying to evaluate a parameter-dependent indefinite integral using a PDE-based scheme I described here, and I'm having some trouble when I try and cut down the domain from a square to a triangle. ...
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### How can I numerically pre-compute an indefinite integral with a parameter?

Suppose I have a function $f(t)$, and I want to compute its indefinite integral $$F(t)=\int_0^tf(\tau)\mathrm d\tau.$$ Moreover, suppose that, for any of a number of reasons, I require this integral ...
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### Split Boundary Value Problems win Algebraic Equations

Is it possible at all to solve with NDSolve (or other built in function) a split boundary value problem with algebraic equations? Please look at the following example: ...
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### Solving a simple ODE [duplicate]

I am trying to solve $y(x)' = \sqrt{y(x)}$ with initial condition $y(0)=0$ for $x\in \mathbb{R}$. I have tried this: DSolve[{y'[x] == Sqrt[y[x]], y[0] == 0}, y[x], x] but this gives {{y[x] -> x^2/4}...
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### Rotating an Interpolating Function

I have used the following code to generate eigenfunctions of a PDE: ...
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### Weird behaviour for a vector InterpolatingFunction inside an NDSolve

I have run into some weird behaviour on the part of NDSolve which I find pretty bizarre and which I would like to understand better. Suppose, for the sake of ...
189 views

### NDSolve memory usage [closed]

I am trying to solve numerically a system of linear ODEs with some quickly varying driving functions. The basic command is: ...
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### Nonlinear coefficients are not supported in this version of NDSolve [duplicate]

Thanks to the answers in other questions, I am aware of the fact that NDSolve produces Nonlinear coefficients are not supported in this version of NDSolve when some boundary conditions are ...
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### Phase Portrait to Differential Equation [closed]

I posted this question on Math.SE and have received a satisfactory answer in the context of that website. I am re-posting it here to get input from Mathematica users. Why would I receive a different ...
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