Questions on the use of numerical functions NIntegrate and NDSolve.

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3
votes
1answer
83 views

NIntegrate on tetrahedron

I've been trying to numerically calculate an integral in a tetrahedron of a discretized domain. In some cases when I specify a method I've been getting the error message NIntegrate::femonly ...
3
votes
2answers
265 views

NIntegrate giving message NIntegrate::slwcon:

I got this interesting answer from Mathematica when trying to integrate my function numerically: f[x_] := Sqrt[17*x^2 + x^4] NIntegrate[f[x], {x, -1, 2}] ...
3
votes
1answer
105 views

NDSolve break condition

I'm solving a differential equation numerically by NDSolve[{p'[r] == -function[r,p[r]], p[0] == pcenter}, p,{r, 0, rmax}] with function>0. At some r, p[r] ...
3
votes
2answers
1k views

How does one specify Neumann conditions for NDSolve?

I have a series of functions defined in my notebook, and then want to use this to solve a diffusion-reaction type equation. At the moment, something like this works: ...
3
votes
2answers
757 views

NDSolve: Normalizing at every step

Suppose I have an transport equation with an initial conditions: ...
3
votes
2answers
78 views

Error control for NDSolve

I have a problem controlling the numerical error associated with the following non-linear ODE : ...
3
votes
1answer
109 views

Evaluating a numerical integration with infinity as limit

I am trying to evaluate a numerical integration (to get an expression of the constant Ω) Suppose that h[x_] := 1/(1 + a x^2) ...
3
votes
1answer
243 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In ...
3
votes
2answers
147 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
3
votes
1answer
109 views

Strange integration

Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ...
3
votes
1answer
503 views

Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
3
votes
1answer
252 views

Integrate equations of motion when force depends on position

I'm fairly new to Mathematica. I'm trying to test my C++ implementation of a fourth order Runge Kutta method for Newton's equations of motion. I want to test my integrator when the applied force is ...
3
votes
1answer
809 views

NDSolve for a large system of simple ODEs

I am solving a system of many (more than 100) ODEs. It is the kind of standard rate equation encountered in semiconductor physics. Here is the system: ...
3
votes
2answers
447 views

How to set the initial condition? (to make IC and BC consistent)

I want to find the initial condition which fits mixed boundary condition of Phi[r, Theta, t]. The original initial condition in text is Phi[r, Theta, 0] == 1 . ...
3
votes
1answer
104 views

NIntegrate and Interval regions

NIntegrate does not seem to like Intervals as regions. Consider the following example function defined for a parameter "a" ...
3
votes
1answer
254 views

Surface area of intersecting spheres

Given a sphere of radius 1 centered at the origin and $n$ spheres with radii $r_i$ centered at predefined coordinates, $c_i$, in space, I am after the surface area of the unit sphere that is not ...
3
votes
1answer
534 views

Question on accuracy and precision of NIntegrate

As a Mathematica newbie, I was testing the accuracy/precision of NIntegrate (9.0.1.0 on Mac) and have obtained a very peculiar result. ...
3
votes
1answer
232 views

NDSolve: Reinitialize fails with If condition

I have found a weird problem using If conditions containing an state inequality of the form state<=. First consider the simple ODE with an If condition ...
3
votes
1answer
1k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
3
votes
1answer
415 views

NIntegrate inside NSum

Consider the following function with a numerical integration: ...
3
votes
1answer
114 views

What boundary is added when NDSolve::bcart pops up?

When insufficient boundary conditions are given to NDSolve for solving PDE, the warning NDSolve::bcart pops up: ...
3
votes
1answer
134 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
3
votes
2answers
144 views

NIntegrate returns zero for non zero integrand, 4d Integration

I am trying to calculate the following integral. ...
3
votes
1answer
1k views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
3
votes
1answer
573 views

How to adjust parameters to experimental data on a NDSolve problem

I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3. ...
3
votes
1answer
200 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
3
votes
1answer
486 views

Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
3
votes
1answer
444 views

Efficient way to perform elementary integration step with NDSolve internal method

I'm trying to tweak the NDSolve function to perform one elementary integration step (using some explicitly selected stepping algorithm via ...
3
votes
0answers
52 views

How to speed up a high dimensional numerical integration of Gaussian-form integrand

My integral has the following form: $$\int \sin(\theta) d\theta d\phi\left| \int d^3p_1 d^3p_2d^3p_3 \frac{f(p,\theta,\phi)}{g(p,\theta,\phi)}e^{-\frac{1}{2}(p^\mathrm{T} .A.p)}\right |^2,$$ where ...
3
votes
0answers
159 views

Obtaining NIntegrate error estimate

Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate? Internally Mathematica must keep track of this error, because it is used to ...
3
votes
0answers
151 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
3
votes
0answers
68 views

Integrate yields complex value, while after variable transformation the result is real. Bug?

I have the follwoing integral: Integrate[1/Sqrt[0.7 + 0.3*(1 + z)^3], {z, 0, Infinity}, Assumptions -> z \[Element] Reals] >> -3.36354 - 3.85013 I the ...
3
votes
0answers
130 views

How to specify the time variable for NDSolve

I recall that it is possible to specify which independent variable is the "time" variable in NDSolve, but I can't find it documented anywhere. Does anyone recall ...
3
votes
0answers
285 views

Function with a sharp resonance which Mathematica fails to integrate. Why?

I'm a new user of Mathematica and I'm trying to use it to calculate the collisional cross-section as a function of energy for a given potential and decay rate. I know that the resulting function ...
3
votes
0answers
160 views

Non-linear integral equation

I'm trying to solve with Mathematica an integral equation. I found this excellent answer (How to solve a non-linear integral equation?) solving with a collocation method a problem which can be ...
3
votes
0answers
1k views

Using NDSolve for Integro-Differential Equations

I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are: ...
3
votes
0answers
455 views

Numerically solving PDE with high precision

I want to numerically solve the PDE $\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$ with some initial and boundary conditions and given parameters $c$, $m$ and $l$. Consider the code ...
3
votes
0answers
237 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
3
votes
0answers
1k views

Solving a system of nonlinear equations self-consistently

I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
2
votes
1answer
828 views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
2
votes
4answers
464 views

How to calculate this integral?

I am trying to Integrate the following Integral : $\int_1^{\infty } \dfrac{\left(x^2-1\right)^{13/2} e^{-ax} }{x^{10}} \, dx \,\, \,\,\,\,\,\,\,\,\,\,\,\,(a=\textrm{real>0})$ Mathematica didn't ...
2
votes
4answers
286 views
2
votes
2answers
1k views

optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
2
votes
3answers
356 views

How can I apply calculus to functions obtained from NDSolve?

Originally, I asked the question below, but the real underlying issue is as follows: When we solve an ODE numerically, I get the answer like this: ...
2
votes
2answers
236 views

NIntegrate piecewise vector function

Is there a way to numerically integrate a vector function defined via Piecewise? Example: ...
2
votes
3answers
96 views

slwcon and eincr in integrating multivariate Gaussian random variables

Why is the following integration involving multivariate Gaussian distribution so slow and generating an error? Is there a better integration strategy? All that I'm doing is considering ...
2
votes
2answers
97 views

Calculate area between two multivalued curves

I have to calculate the area between two curves which will give me the result of a particular quantity. However, both the curves are multivalued functions. Here is a data set showing the region where ...
2
votes
2answers
211 views

Plot result of non analytical-integral

I have the following function: h = 1; c = 1; k = 1; B2 = (2*h*c^2)/(x^5 (Exp[(h*c)/(x*k*T)] - 1)); (someone can see that this integral is the Planck function). ...
2
votes
2answers
118 views

FindFit working with Integrate but not NIntegrate - I am using “?NumericQ”

I'm having some syntax problems with finding a fit to an equation that doesn't have an analytical expression for it's integral. Because I think the problem is one of syntax, I am substituting a ...
2
votes
2answers
428 views

How to compute this triple integral? [closed]

In Mathematica how can I compute this integral:$$ \iiint_{D}\sqrt{(1-9z^2)(1-4y^2-9z^2)}\,dx\,dy\,dz$$ where D is the domain: $$D: x^2 +4y^2+9z^2\le1$$ Please I need help!!!