# Tagged Questions

Questions on the use of numerical functions NIntegrate and NDSolve.

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### Nintegrate has memory leak

Bug introduced in 6.0 and fixed in 10.2.0 NIntegrates uses memory and does not release it. For long loops with NIntegrate ...
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### 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 $\dot{x}=f(x), \quad \dot{y}=g(x,y)$ ...
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### How to improve the solution of a double pendulum system

First, the code: ...
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### 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. ...
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### Solving an equation involving an integral

How do I get the following into Mathematica, solving for $a$: $$0.7 = 1 - \frac{2}{a} \times \left[ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1}\mathrm dx + \frac{a}{6} - 1\right]$$
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### triple NIntegrate fails

Here's m problem simpler in terms of codes ...
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### Stategies to avoid NIntegrate::slwcon error

I am trying to numerically evaluate an integral whose integrand depends on two parameters, say $(a,b)$ and when $b\gg 1$ I suspect (although it's not guaranteed) that the integrand is very small. Thus ...
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### Why does Mathematica give the wrong answer when integrating?

Bug introduced in 8.0 or earlier and fixed in 9.0.0 I integrate Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}] Mathematica gives: ...
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### How to do multi-dimensional principal value integration?

The toy model is: $$\int_{-2}^{2}\int_{-2}^{2}\frac{1}{1-(x^2+y^2)}\, dx\, dy$$ The integrand have opposite sign across the circle $x^2+y^2=1$, so one would expect that the integral has meaning only ...
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### Integrate yielding a ConditionalExpression but I don't think the condition is necessary

Suppose I take the PDF of the LogNormal distribution with parameters m and s evaluated at x. I obviously get an expression involving m. I now want to integrate that expression not with respect to x ...
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### 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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### Conditional numerical integration boundaries

I have a multidimensional integration of the form: ...
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### 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 ...
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### Slow exponential evaluation over lists

This question,which is still unanswered, might be relevant because it involves NIntegrate over lists and it also has Exp. In ...
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### 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: ...
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### 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 ...
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### Numerical integration with NIntegrate

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I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ \frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda ...