Questions on the use of numerical functions NIntegrate and NDSolve.

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Integration of Two Manipulatable Cylinders

Introduction I created the following code to simulate the many possible interactions between a cylindrical protein crystal and a x-ray beam during serial femtosecond crystallography. ...
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2answers
187 views

Integrating a list of functions

For the purpose of this minimal example, let's say we have a list of functions, like this: f[y_?NumericQ] := {NIntegrate[z*y, {z, 0, 1}], a y} I want to ...
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2answers
96 views

How to add (energy) constraint when using NDSolve to Equation of Motion

To simplify my problem, I will try and solve the Equation of Motion for a particle in a 1D Harmonic Potential. energy[x_, p_, m_, ω_] := p^2/(2 m) + (m ω^2)/2 x^2 ...
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2answers
353 views

Calculating the area under a curve, but above a certain threshold value

so here I am with a time series of data (hours (t) and corresponding measurements (a)). ...
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1answer
429 views
5
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1answer
2k views

How do I prevent NIntegrate::inumr errors within other functions?

I believe this question is best illustrated with a simple example. If I run FunctionInterpolation[NIntegrate[a + b, {a, 0, 1}], {b, 0, 1}] I get errors of the ...
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1answer
107 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
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1answer
525 views

Unexpected results from NDSolve

I am trying to solve a stiff reaction diffusion system with NDSolve. However, it does not produce the expected results. My problem is a spherical cell with 5 ...
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2answers
520 views

Numerical Integration as Model for Nonlinear Fit

I'm trying to do a fit for parameters of a function within an integral but I'm getting errors when I try and run it. Essentially I want the following fit to work out: ...
5
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1answer
406 views

Solving homogeneous Fredholm Equation of the second kind

I am trying to solve a homogeneous Fredholm integral equation of the second kind, i.e. $\lambda y(x) = \int\limits_a^b e^{i[\phi(t)+k(t-x/M)^2]} y(t)\,dt$ where $\lambda$ is the eigenvalue (to be ...
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1answer
922 views

Solve system of ordinary differential equations that doesn't have an initial condition (t=0), but has an inifinity condition (t=infinity)?

I have a question for solving t -> Infinity on Mathematica. First, I have a system of ODEs: ...
5
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2answers
298 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
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1answer
133 views
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3k views

How to handle NDSolve::ndsz problem (singularity problem)

I have 2 second order differential equations (non-linear). The physics behind them is correct. I verified the equations many times. It is a solid pendulum with a mass-spring at the end of it. Now, ...
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1answer
106 views

Finding minimum fly-by radius between Mars and spacecraft from interpolating function

I've written an interplanetary trajectory solver/plotter that plots the path taken by a spacecraft on an Earth-Mars mission, but have run into a little trouble when the spacecraft actually reaches ...
5
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1answer
302 views

Proper use of arbitrary number of variables

So, I'm working on a project where the number of independent variables is not fixed. Consider a problem of $N$ independent variables, $\boldsymbol{r}$. I want to perform different things with them. ...
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0answers
122 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
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86 views

Modify NDSolve`StateData (if possible)

I am trying to solve a PDE that needs to be scaled constantly (refer to this). @andre suggests I modify NDSolve`StateData. Now, the problem is, I'm not used to ...
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2answers
777 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.
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2answers
238 views

Approximate value for the area between the curve

I've got this task: Use Mathematica to obtain an approximate value for the area between the curve $y=1/4$ and the x-axis over the interval $[1,2]$ with $50$ subintervals using the left ...
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2answers
639 views

How to solve for an Z-Score of a T-Distribution?

I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, ...
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5answers
418 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 ...
4
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5answers
415 views

NIntegrate::slwcon Problem

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate[] needs a lot of time to calculate this. Is there any way to ...
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4answers
1k views

Numerical differentiation methods

Is it possible to write a code in Mathematica that implements various differentiation methods (like forward, central, extrapolated, etc.)?
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3answers
422 views

Find arc length

I am trying to find the arc length for using ...
4
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1answer
684 views

Is it possible to calculate a Lebesgue integral in Mathematica?

As the title says, I wonder if it is possible to calculate a Lebesgue integral in Mathematica, especially when the domain of integration is $\mathbb{R}^N$, or in other words multivatiate Lebesgue ...
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2answers
167 views

LevinRule and SphericalBessels

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on ...
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3answers
338 views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...
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2answers
125 views

NDSolve not returning the expected solution

I'm trying to simulate a simple circuit with Mathematica. The equation of the circuit is $R \dfrac{dQ}{dt} + \dfrac{Q(t)}{C} = f_{sig}(t)$. This is the definition of $f_{sign}$, and the function ...
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1answer
245 views

Integral of integral — it takes too much time

When I evaluate the following expression in Mathematica, it takes so much time that I don't want to wait for the evaluation to complete. So I think that there must be a better approach. ...
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2answers
252 views

How to use NIntegrate when there are symbolic constant coefficients

I would like to numerically integrate an equation such as the one below in which there are symbolic constant coefficients. I used a very simple code but it doesn't work in general, that tried to deal ...
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3answers
570 views

Numerical solution of a differential equation with NIntegrate coefficients

I am trying to solve a linear ODE with a variable coefficient which is given in terms of an integral I can only do numerically. That is, I have an equation of the form $$ ...
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1answer
173 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...
4
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2answers
114 views

How to plot a function that is not defined after certain point

I'm plotting a function that I get after numerically integrating over another function. Something like: f[x_,y_]:=NIntegrate[g[x,y,z],{z,0,1}] I know that above ...
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2answers
131 views

Compute the average distance from the base of a rectangular pyramid to its apex

How can I compute the average distance from the base of a rectangular pyramid to its apex? For example, if the base of the pyramid is 30 feet by 8 feet, and the height of the pyramid is 12 feet, then ...
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1answer
365 views

Differential Equations with Matrices

I'm trying to implement the differential equation of a Cellular Neural Network in Mathematica as seen below: ...
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1answer
1k views

Incorrect solution of diffusion equation with Neumann boundary conditions

I want to set up a PDE model, which takes a two-dimensional diffusion equation into account. The key problem is that I have some trouble in solving the two-dimensional diffusion equation numerically. ...
4
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1answer
104 views

How to use WhenEvent with a vector ODE in NDSolve

I have an ODE system I'd like to specify as a vector equation in NDSolve. I'm not clear on how to use WhenEvent for a system ...
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2answers
508 views

WhenEvent in NDSolve

How come this doesn't work as I intended? ...
4
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1answer
194 views

How to find derivative of a numerical solution, where precision is ambiguous?

I am trying to take the derivative of a numerical solution. I am concerned that the way I'm doing this may be problematic due to numerical error; I think there must be a better way but I'm not very ...
4
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1answer
127 views

Solution to a T+U = E equation

I needed to solve really easy differential equation (in dimensionless units): $$ \mathcal{T} (\dot{\xi}) + \mathcal{U} (\xi) = \text{const.} \equiv \varepsilon ; \quad T(\dot{\xi}) = \dot{\xi}^2 ; ...
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1answer
113 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
4
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1answer
189 views

Find lengths of contours in a ContourPlot

I am trying to find the lengths of different contours in the following plot: It is a complicated piecewise function evaluated on the unit disk. I am hoping there is an easy, generalized way to ...
4
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1answer
229 views

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: ...
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2answers
515 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
4
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1answer
187 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 ...
4
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1answer
318 views

Error Interpretation in NIntegrate

I am using a recursion algorithm developed by Migdal for Lattice Field Theory, and I have the following code: ...
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2answers
778 views

How to Solve this ODE with Mixed Boundary condition

I have an ODE equation which is sort of y''[x] + 2 y'[x]/x + .0001 (y[x])^3 ==0 subject to the boundary conditions ...
4
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1answer
77 views

Possible bug / numerical issues with HypergeometricU — any suggestions for a fast workaround?

I've encountered some problematic behaviour with HypergeometricU. I have a probability distribution on the positive integers that takes the following form after ...