Questions on the use of numerical functions NIntegrate and NDSolve.

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7
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1answer
482 views

Speeding up numerical Fourier Transform

I wrote this function NFourierTransform, which takes a function $f(k)$ and numerically calculates the fourier transform integral for discrete values of $k \in ...
7
votes
2answers
255 views

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: ...
7
votes
2answers
472 views

How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
7
votes
2answers
275 views

Problem with NIntegrate when WorkingPrecision is specified

I am trying to evaluate this integral numerically: $$ \int_0^{\infty } m \exp (-m) J_1(m){}^2 \, dm $$ Everything is OK when only the integration method is specified: ...
7
votes
1answer
71 views

Unify the sampling of NIntegrate[ {f, g, h} w ]

I'm trying to numerically integrate a function which has a vector-valued slow part and a much faster component which is shared by all the components, i.e. an integral of the form $$ ...
7
votes
1answer
394 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
7
votes
1answer
522 views

Determining which rule NIntegrate selects automatically

I need to numerically integrate a highly oscillatory function over the semi-infinite domain $(0,\infty)$: $$\int_0^\infty \frac{\sin^2(x) \sin^2(1000 x)}{x^{5/2}}\mathrm dx$$ Since the Levin rule ...
7
votes
1answer
255 views

Fitting a numerical integral via NonLinearModelFit to magnetic data

I'm new to Mathematica and I'm currently trying to fit $$m_T (H,T) = N_T \int\limits_0^{\infty} \frac{x k_\text{B} T}{\mu_0 H} \mathcal{L}(x) \text{pdf}(D_\text{mag}) \text{d}D_\text{mag}$$ with ...
7
votes
1answer
312 views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
7
votes
0answers
335 views

NDSolve::ndcf: Repeated convergence test failure. How to solve?

I am trying to simulate a system of $n$ pendulums with some friction in Mathematica 9. This is the code I am using: ...
7
votes
0answers
2k views

Integro-differential equation

I have to numerically solve a nonlinear partial integro-differential equation using Mathematica. This is my equation, $$\frac{\partial y(x,t)}{\partial t}=\int_{-\infty}^\infty K_0(|x-u|) ...
6
votes
2answers
395 views

Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from tmin=0 to ...
6
votes
2answers
398 views

How to work out the parameter in a definite integration which has an exact value while the integration doesn't have an analytical solution?

Here is the equation I'm trying to solve: NIntegrate[1/(E^(1/(λ T)) - 1), {λ, 200, 220}] == 1000 T is the parameter I'm ...
6
votes
3answers
952 views

Strategies to solve an oscillatory integrand only known numerically

I have an integrand that looks like this: the details of computation are complicated but I only know the integrand numerically (I use NDSolve to solve second ...
6
votes
2answers
264 views

Catching only the first event in NDSolve EventLocator

I have a system of ODEs that I solve. During the integration process, there's an event that I want to catch, but I want to (a) continue the integration after the event and (b) catch only the first ...
6
votes
2answers
1k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
6
votes
2answers
657 views

How to set the NDSolve method to LSODA

I notice that off all the Method options available for NDSolve[...], LSODA is invoked quite ...
6
votes
1answer
575 views

Using a compiled function inside NIntegrate gives “CompiledFunction::cfsa” message

The following function is defined for Real input: FFc = Compile[{{x, _Real}, {EF, _Real}},If[x > EF, 0., If[x == EF, 0.5, 1.]]] FFc is now used in the ...
6
votes
2answers
1k 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 ...
6
votes
2answers
248 views

Cannot Get Numerical Results to Match

I try this numerical summation (in two parts) ...
6
votes
1answer
276 views

Getting Integrate to perform numerical integration

I am trying to calculate the mutual impedance of two antennas which is just a big integral. I defined my function in terms of my variable, but when I execute it, Mathematica runs for a while and then ...
6
votes
1answer
322 views

What does MaxStepFraction do?

I find that with NDSolve[...] while solving a partial differential equation, changing the MaxStepFraction from ...
6
votes
1answer
182 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 ...
6
votes
1answer
400 views

The difference between “SymbolicProcessing” -> 0 and restricting the function definition to numeric values only

The Documentation tells us that there are two ways to disable symbolic processing of the integrand by the NIntegrate function when it is known that it just slows ...
6
votes
2answers
332 views

NDSolve Plotting issue

I am trying to solve a system of ODEs with one extra boundary condition. ...
6
votes
0answers
76 views

Slow NIntegrate over complicated domains (sometimes)

Overview I have a very large matrix I need to calculate where each element requires the integration of a product of two functions over some complicated domain. I would like to find a set of options ...
6
votes
0answers
383 views

Numerically solve 2nd order differential equation with singularity

Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example: $$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$ where ...
6
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0answers
417 views

Optimizing NIntegrate for higher PrecisionGoal

By default, NIntegrate works with MachinePrecision and its PrecisionGoal is set to ...
5
votes
3answers
841 views

How to speed up the plot of NIntegrate?

Here is a toy example: f[t_] := NIntegrate[Sin[x], {x, 0, t}]; Plot[f[t], {t, 0, 10}] // Timing Even such a simple example will take 2.8 seconds on my computer. ...
5
votes
3answers
275 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m ...
5
votes
1answer
1k views

NDSolve, Schrödinger equation, and decaying solution

I am trying to solve a Schrödinger equation for a particle hitting a step potential using NDSolve in Mathematica. Here is my code: ...
5
votes
2answers
638 views

How to deal with zero in NDSolve in mathematica?

I would like to solve the following ODEs $$\begin{cases} x'(t)&=y\\ y'(t)&=-y(t)/t-e^{x(t)},\\ x(0)&=1,\\y(0)&=0, \end{cases}$$ (EDIT : The second equation used to be $y'(t) = ...
5
votes
3answers
1k views

How to use results of NDsolve[] for further solving of ODEs?

I have a system of ODEs with 10 eqns. I can solve the first 5 independently. How can I use those results to solve for the remaining 5? An easy example would be $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
5
votes
1answer
278 views

NDSolve and WhenEvent Causing Excess Work

When I use the following system model = {x'[t] == x[t] (1 - x[t]) - x[t] y[t], y'[t] == x[t] y[t] - y[t], x[0] == 0.5, y[0] == 0.5} with the ...
5
votes
2answers
308 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
5
votes
2answers
183 views

Triple fractional part-related integral

The evaluation with Maple suggests the triple integral is around $1$, but Mathematica tells it's $0.0958758$. When using the code ...
5
votes
1answer
190 views

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. ...
5
votes
2answers
163 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 ...
5
votes
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 ...
5
votes
1answer
453 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 ...
5
votes
1answer
794 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
votes
1answer
119 views
5
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1answer
98 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
votes
1answer
271 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. ...
5
votes
0answers
84 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 ...
5
votes
0answers
681 views

Controlling the time step in NDSolve?

I generally use NDSolve for stiff non linear partial differential equations of 4th order. I find that a BDF1 method generally does well to placate my beast of a PDE. I've also tried out ...
4
votes
2answers
664 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.
4
votes
2answers
578 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, ...
4
votes
5answers
366 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 ...