# Questions tagged [differential-equations]

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

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### Formulating equations for 3D stress in the finite element method

I would like to know how you formulate equations for the finite element method for stress calculations. We know the answer because user21 has put it here. It involves usage of ...
194 views

### Solving linear coupled PDEs by FDM

I am trying to solve some linear, coupled PDEs for perturbative analysis (first order in time, 3rd order in space), for which I then plan to take the global spatial maxima of their magnitudes and plot ...
81 views

### NDSolve cannot evolve Gaussian wave packet with small width

I want to solve a 1d wave equation with initial conditions: $$u(x,0) = f(x) = e^{-(x - x0)^2/2\sigma^2} \ \ \text{and}\\ u_t(x,0) = - f_x(x)$$ The second condition is the advection equation and ...
62 views

### WhenEvent ignores some actions

I've got a problem where WhenEvent successfully detects an event, but then performs only some of the actions. In this minimal example, ...
54 views

### Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
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### How to put solutions of mutiple DEs with NDSolve in table

I have $N$ differential equation for each $s \in {1,2,...,N}$ on the domain $x \in [1,2]$ of the form (e.g.) $xf_s'(x) + \log(xs) f_s(x)+1 = 0$, with the boundary condition $f_s(1) = e^{-s}$ Now I ...
87 views

### Mathematica running out of RAM while executing NDSolve

I am playing with Mathematica to solve the 2D-wave equation with the code below: ...
443 views

### Plot exactly N bounce of a ball

I want to plot exactly N bounce of a ball. I'm using DSolve to solve the differential equation and WhenEvent to change the velocity. The code below plots only the first 10 seconds. ...
40 views

### NDSolve: evolutionary singularity in coupled differential equations

I am trying to solve coupled differential equation where a function attains a value such that its derivative is infinite. ...
665 views

### How to plot an unstable attractor?

I'm trying to solve and plot the following in Mathematica: ...
326 views

### Nonlinear boundary value problem of ODE involving principal value of integral

I have asked a question on a nonlinear eigenvalue problem (EVP). And I have worked on these for a week but I cannot solve it. I think I should first try to solve the related ODE boundary value problem ...
199 views

### Fitting multiple data with model and NDSolve with different initial conditions, and other shared parameters

I know that there are already questions about fitting multiple datasets and about NDSolve and about shared and non shared parameters, but I tried to apply them and some things are still not clear. ...
54 views

### Fitting system of differential rate equations to data

I am trying to fit a set of differential equations to experimental data, without luck so far. These are the data: ...
46 views

### Evaluation Control for Equation Input to NDSolve

I am trying to numerically integrate a system of equations using NDSolve and am having issues with symbolic matrix inversion taking a long time. The actual system is much more complicated, but I have ...
36 views

### Calculation of evolution equation with NDSolve

I have near to no experience with mathematica, so this might seem pretty trivial. I want to solve an Evolution equation, i.e. we have a function $f(t,x)$ and a differential operator $T(t,\partial_t)$. ...
50 views

### ParametricNDSolve many functions and plotting

I don't understand why I don't get the plots : ...
60 views

### NDSove vs ParametricNDSolve

ParametricNDSolve is very practical when one has to execute NDSolve again and again. However is it equally accurate? I have not ...
55 views

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### WhenEvent versus If function for ODEs

The following equation works for ParametricNDSolve ...
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### DSolve behaves weirdly with dynamic [duplicate]

I am an beginner in using dynamics as well as mathematica. I am trying to ask mathematica to solve and plot the solution of X'=AX with dynamic every time my matrix A updates. However the Dsolve ...
113 views

### How do I solve a certain differential equation?

I need to find out a solution to the equation: z r[z] r''[z] - (d - 1) r[z] (r'[z])^3 - (d-2) z (r'[z])^2 - (d - 1) r[z] r'[z] - (d - 2) z == 0 subject to the ...
54 views

### Problem with NDSolve and Manipulate function

I'm having an issue with commands NDSolve and Manipulate. I'm trying to represent the rotation spin, nutation and precession of a spinning top (approximated to an inverted cone). Under specific data ...
112 views

### Fitting experimental data with a parametric function

How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below: First let's generate some data: ...
89 views

### ParametricFunction from ParametricNDSolveValue changes when evaluated?

I am new to using ParametricNDSolveValue (and ParametricFunctions in general), so I am hoping that I have made a simple error. First I set up a system of differential equations: ...
45 views

### How to provide a system of input every x time interval (e.g, x=1 week)

The following code described an input to the system only during t less than minInfusionTime after time zero. Any way to give this same input every x time (e.g. every week) after time of zero, to an ...
64 views

### DSolve not working on vector equation

Ok, so I'm trying to solve a differential equation of motion, and mathematica doesn't do anything to my input. It just leaves it unevaluated. I know that the system is physically solvable with not ...
143 views

### Non Linear Model Fit - Fitting ODE to Data

Thank you everyone for your meaningful contributions! My Goal and Problem I'm trying to fit a particular ODE in a set of ODE's to experimental data. I've attempted to implement this by following the ...
65 views

### Parametric Find Maximum

I'd like to plot the maximum of a curve in function of a parameter. Meaning I looking for maxima that depend on a parameter. Here is what I tried to do but FindMaximum is not parametric, so it did ...