# Tagged Questions

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### Understanding of method for NDSolve

I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use: ...
85 views

### Calculating the Lyapunov Exponent/Spectrum for the Duffing Oscillator

Some fellow students and I are trying to calculate and plot the Lyapunov spectrum for the Duffing oscillator (currently a test approach). Each of us has Mathematica knowledge based purely on past ...
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### Solution of Coupled Second Order ODEs with Boundary Conditions

D[Tu1[x], {x, 2}] qu - Tu1[x] (fu0 + I w p) == Tou[x] f1 D[T1[x], {x, 2}] q - T1[x] (f0 - b g0 + I w p)== To[x] (f1 - b g1) - g1 For T1 , ...
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### NDSolve accuracy related problem

I want to solve this equation: ...
48 views

### Discrete sampling of interpolating function returned by NDSolve

When solving an ODE with NDSolve, Mathematica returns an interpolation function. I need a discrete sampling of this function however. Naively, I can write this as (example): ...
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### periodicity of a solution of ndsolve pde

I am solving a pde with NDSolve and the solution is like U(x,t) which seems to be periodic and I am trying to find an algorithm to find the periodicity of such numerical solution. my code is like ...
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### Boundary Value Problem- using NDSolve or another method

I am trying to solve a set of coupled partial differential equations, with defined boundary conditions using mathematica. Here are the equations and the boundary conditions. ...
42 views

### Invariant error plot for an arbitray system of ODE

i try to use InvariantErrorPlot command for a generic system of ODE but i find only example with pre-building equations from Mathematica Packages. This is one of ...
90 views

### Initial and boundary value errors

NDSolve::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> I keep getting this, ...
606 views

### Plot Matlab icon

I started to explore this on a whim and hasn't succeeded yet… Some introduction for the icon is found here but I can't understand it very well. (I admit that, though playing with ...
86 views

### Infinite expression 1/0.^(1/4) encountered in NDSolve

I am trying to solve very simple system of coupled differential equations using the NDSolve function, but I am getting ...
117 views

### Using NDSolve for three variables as function of time

I want to be able to plot z, and r. Should I be using DSolve, NDSolve or something else? I've tried to clear it up a bit Thanks, Will ...
87 views

### Boundary condition is not specified on a single edge of the boundary of the domain

I am attempting to solve a PDE as prescribed in a paper I am reading; however, Mathematica doesn't seem to be happy with the way I am posing the problem. Im my case, r(t,100) is an approximation of ...
172 views

### How to choose MaxStepFraction for optimal speed of NDSolve

I'm trying to use NDSolve to solve a 1D Schrodinger's equation, and it seems that MaxStepFraction has huge effect on the ...
74 views

### Differential equation with random variable

How can I derive analytically or compute numerically the solution to following differential equation $$dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X$$ where X is a random variable (e.g. from a ...
400 views

### shooting method and stifness problem for NDSolve

I'm trying to solve numerically the following differential equation: 1/r[x]^5 + k/Sqrt[1 + r'[x]^2] - (k r[x]r''[x])/(1 + r'[x]^2)^(3/2) == 0 I can set boundary ...
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### How to solve initial value problem using Runge-Kutta method? [duplicate]

How to solve the following initial value problem using Runge-Kutta method u''[x] + (2/x) u'[x] + E^(u[x]) == 0, u[0] == 0, u'[0] == 0
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### Transformation of the NDSolve result into new dependent variables

I have solved a set of coupled differential equations and now I need to convert them into different dependent variables and sketch their trajectories. Here is the code I have written so far: ...
335 views

### Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
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### Jumps in NDSolve results

I need to compute using NDSolve routine, some function $F(x)$, having two possible values $F_1(x)$ and $F_2(x)$ depending on whether the argument exceeds some ...
262 views

### Avoiding zero (empty set) solution with NDSolve

I'm trying to use NDSolve for a chemical kinetics equation where the rate of conversion is given by this relationship as typed in Mathematica: ...
155 views

### Defining extra boundary conditions for NDSolve?

I have a second order reaction / diffusion type ODE of the form $\frac{D_{o}}{r^2} \frac{d}{dr}\left(r^2 \frac{dC}{dr} \right) - \frac{aC}{C+k} = 0$ where $a, k$ and $D_{o}$ are constants and $C$ is ...
234 views

### NDSolve: ProcessEquations and Reinitialize with Piecewise functions

I am having trouble with using NDSolveReinitialize when the system consists of a pieceise function. If we define the ODE system ...
192 views

### Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
156 views

### How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...
295 views

### Crank-Nicolson with NDSolve?

As far as I understand, the Crank-Nicolson method (a.k.a. trapezoidal method) can be expressed as a second order implicit Runge-Kutta method. It's Butcher tableau is: ...
157 views

### Using new symbol in WhenEvent in NDSolve

This is an example in Mathematica's help document. ...
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### Adding a constant vector to a vector differential equation seems to break NDSolve. Why?

I'm trying to solve a differential equation that's phrased in terms of matrices and vectors. My minimum working example is this: ...
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### singularity in NDSolve for some values of parameter

my equation is: ...
320 views

### Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: i \frac{\partial \psi}{\partial t} = \left[ ...
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### Are FEM methods integrated in NDSolve yet? [duplicate]

About a year ago there was a discussion on these forums as to whether FEM methods have already been integrated into NDSolve in Mathematica. The answer back then was ...
1k views

### Complex valued 2+1D PDE Schroedinger equation, numerical method for NDSolve?

Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schroedinger) equation, for the free particle propagation of an initial wavepacket. ...
161 views

### Specifying mesh in NDSolve

I am trying to solve a system of one-dimensional two-point boundary-value problems with NDSolve. I would like use a fixed mesh (specified by me) in the calculation. Is there a way to do this? The ...
198 views

### Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
403 views

### Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows \$\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
594 views

### Does Mathematica have a command analogous to ode45 of MATLAB?

Does anybody know if Mathematica has an analogue of MATLAB's ode45 command? I need to solve a second order coupled ODE system of equations.
111 views

### Integrating and plotting pde system solution

I have a trouble with plotting a pde system solution. I'm solving a PDE system in 2-dimensional space and then I want to integrate the solution along one dimension and build a log plot along the ...
208 views

### WhenEvent and partial derivatives

Can WhenEvent be used to reset the conditions on a PDE at a given time? How would the syntax of that be? This is the code Im using ...
878 views

### Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
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### How to let Mathematica computes the limit if it encounters an indefinite expression when solving ODEs?

The code talks itself clearly: ...