Questions on the use of numerical functions NIntegrate and NDSolve.

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2
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0answers
299 views

Is mathematica storing information it shouldn't store?

I'm seeking to find solutions to a numerical integration with a large set of parameter combinations (basically, I'm doing a brute parameter sampling). Yet, I believe the memory of the computer is ...
2
votes
0answers
401 views

Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
2
votes
1answer
387 views

Directional derivative of SiegelTheta

I'm working on a problem where I have to integrate both the Mathematica function SiegelTheta and some of its second order directional derivatives. Using the function works well but something goes ...
2
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0answers
395 views

FindRoot - Speed and errors

I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
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0answers
865 views

Inconsistent boundary and initial conditions: BC ignored altogether

Consider the following diffusion-decay equation with von Neumann b/c in the origin and Dirichlet at the other boundary: ...
2
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0answers
203 views

EventLocator with LSODA?

Is the EventLocator option not compatible with LSODA on NDSolve. Below is what I tried to do ...
1
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2answers
690 views

Computing 10-dimensional volume of a 9-sphere [closed]

I'm trying to compute 10-dimensional volume of a 9-sphere with radius r using Monte Carlo. ...
1
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2answers
118 views

Trapezoid Integration over a list of pairs [duplicate]

I have two very connected questions: Is there really no built-in function to integrate a list of pairs without converting to a function? Something like: ...
1
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3answers
309 views

plotting an Integration output

How to solve this integral by Mathematica even by numerical methods (plotting the solution) Integrate[(Cos[x] - a)/(1 + a^2 - 2*a*Cos[x])^1.5, {x, 0, 2*Pi}] It ...
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2answers
166 views

How do I exclude regions from numeric integration on Mathematica?

The part of the equation that is giving me trouble is below: f[t_,v_]:= Exp[-(1/Log[1-t/v]^2)]*(v-t) I need to integrate this function over the ranges .1 ...
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3answers
116 views

I know the lower limit of an integration as well as the integral. How to find the upper limit of the integration?

I used the following code. NV[x1_, x2_] := NIntegrate[3 x^2, {x, x1, x2}] FindRoot[NV[0, t] == 3, {t, .001}, PrecisionGoal -> 20] Output: ...
1
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2answers
361 views

Real integral evaluates to imaginary number

The following integral:Integrate[Exp[-2/3 Log[1 + x^3]], {x, 0, 1}] is evaluating to an imaginary number. Its closed-form expression should be ...
1
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2answers
110 views

Simple integration with assumption

I would like to evaluate the following simple expression NIntegrate[Re[Exp[I*Omega*t]], {t, 0, 2 Pi}] for Omega real, but ...
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1answer
128 views

How to prevent tiny complex errors in Integrate?

Integrate is adding a tiny imaginary error to an easy result. Why? And how can I stop it? ...
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2answers
108 views

Evaluation of a large integral

I have a complicated large integral I want to evaluate (does not have a closed form, need an approximation), but Mathematica seems to keep "Running...". Is there any way to make Mathematica use more ...
1
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2answers
488 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
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3answers
2k views

Solve for variable in integral limit when using NIntegrate

I am trying to solve for a variable which appears in the limits of an integral, rather like in the following; ...
1
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1answer
162 views

How do I plot this 3-D, double integral?

I have the following function: I need to plot a 3-D with coordinates f (p, q), p and q. I mean, I enter values for p and q, so that the integral of f (p, q) must be a number. This number must be ...
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2answers
185 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
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1answer
198 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
1
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1answer
1k views

NIntegrate fails while Integrate works

I have a function $f(t)$ defined as $f(t)=\int\limits_0^t(t-\xi)^{\alpha-1}\ \cos(\xi)\ d\xi$ where $0<\alpha<1$. I now want to evaluate this integral at various values of time. Therefore, my ...
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1answer
761 views
1
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2answers
391 views

Numerical Integration in Laplace domain

I need to calculate two different integrals containing a Bessel function in the Laplace domain. I have tried different kinds of quadrature but didn't have any luck. I don’t know how to help ...
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1answer
213 views

NIntegrate is resetting my variables and not giving me a result?

I am trying to check if mass conservation holds by integrating the area under a curve but to no avail. ...
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2answers
98 views

Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral $$\int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x ...
1
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1answer
108 views

How to Minimize an NIntegral

My problem is to minimize in Mathematica a numerical integral. The command FindMinimum[With[{R=2.5},NIntegrate[(R*r1*a)*Sin[r1*a],{r1,1,R}]],a] does calculate ...
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1answer
62 views

NIntegrate::inumri: error [closed]

I am getting the following error: NIntegrate::inumri: The integrand c (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- (1+Times[<<2>>])^0.5)) (1-0.6 (1-(1+Times[<<2>>])^0.5)-0.4 (1- ...
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2answers
129 views

Integral too oscillatory

Is there any way top make this integral less oscillatory? ...
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2answers
122 views

optimization of CountourPlot with NIntegrate

I have to use ContourPlot with a complicated function depending on 2 parametrs (that I cannot report here) that contains numerical integrations. Here is a simple ...
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2answers
634 views

NDSolve with Explicit, Implicit Euler and Trapezoidal method

I am using Mathematica 9.0 both on Linux and Windows and I would like to integrate the Van der Pol equation numerically using various techniques such as Explicit and Implicit Euler and Trapezoidal ...
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1answer
152 views

Computer freezes during NIntegrate[]

I have a notebook that freezes the computer every time I run it (I mean the whole computer becomes unresponsive and do not react to ctrl-shift-esc and ctr-alt-delete as well as alt-tab and ...
1
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1answer
210 views

Orthogonalizing polynomials with inner product depending on parameters

I need to orthogonalize the polynomials $h_n(x)=x^{2n}(1+x^2)^{-4S}$ with $x\in\textbf{R}$, $2S\in\textbf{N}$ and $n\in\{1,3,5,\ldots, 4S-1\}$ over the inner product $\langle h_n,h_m\rangle=32\pi ...
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2answers
53 views

Export NDSolve data

I have calculated a solution of a system of differential equations using NDSolve and generated a plot. How could I extract the data of the solutions? The input is ...
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1answer
45 views

numerical integration errors

I have plotted the following integrals with numerical integration nicely without any error: ...
1
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1answer
98 views

Problem with NIntegrate and FindFit [closed]

I fit the experimental curve with the model using the following equation, ...
1
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2answers
138 views

How to determine the parameter in a differential equation with some fixed solution

Assuming that I have a ODE system with undetermined parameter $$x''(t) == y(t) x(t)$$ $$y'(t) == 2 - a x(t)$$ and I have some fixed solution condition $$x(0)=0$$ $$x(10)=8$$ $$y(10)=3.5$$ Is there ...
1
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2answers
260 views

Plotting a parametric function containing an integral [closed]

I need to plot this expression $$ \phi(s; H,B)=\left(\int_{0}^{s}\frac{1+B\ \sin2H\ t}{\sqrt{1+B^2+2B\sin2H\ t}} \text{d} t,\ \frac{1}{2H}\sqrt{1+B^2+2B\sin2H\ s}\right)$$ for $H=0.5$, $B=0, 0.5, 1, ...
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2answers
94 views

Confusion in Numerical Integration while using FindRoot

I used this code for numerical integration NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, 13}] when upperlimit of x is 13, the integral value ...
1
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1answer
100 views

InterpolatingFunction used to work with mathematic 7 but not working with mathematica 10

This code is used to work perfectly with Mathematica 7 and now it is not working with Mathematica 10. Any help is appreciated. CL05 = InterpolatingFunction[{{0.5, 11.99999999999999}}, {1, ...
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3answers
252 views

Speed up NIntegrate, which takes eigenvalues from another function

I have simplified my problem here, in my actual problem the matrix is much bigger which makes it impossible to find eigenvalues analytically. So, I chose standard BCS problem (2x2 matrix) to ...
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1answer
73 views

numerical integration question

The actual expressions is quite complicated so I will use a trivial example. Let In[36]:= f[u_] := 1/3 - (5/18)*(Cos[u]*a[1] + Sin[u]*b[1])^2 Then ...
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2answers
137 views

Output of NIntegrate depends on MaxRecursion

I have an integral in this form: ...
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2answers
140 views

Numerical integration of modified bessel function

I need to compute the following integral: NIntegrate[ BesselI[-nu, k x]/x ,{x, r1, r}] in which nu=-(2m-1)/2 and I have to ...
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2answers
137 views

Plot3D and NIntegrate issues

f[x_, y_] := 2*x - y Plot3D[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] NIntegrate[f[x, y], {x, -1*Sqrt[4 - y^2], Sqrt[4 - y^2]}, {y, -2, 2}] I ...
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1answer
156 views

How to evaluate complex numerical integral in mathematica?

I have an integral of the form \begin{align} F(\omega) = \int_0^{\infty} f(s,\omega) \mathrm{d}s \end{align} which I would like to numerically evaluate and plot for a range of $\omega \in ...
1
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1answer
309 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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1answer
1k views

Euler's method for system of differential equation

I need to program Euler's method to solve a system of two diffferential equations of first order. Fist, I have programmed the Euler's method for just one differential equation: ...
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2answers
306 views

How to numerically integrate this integral?

I want to integrate a function (spherical coordinates): $$\int _0^{2 \pi }\int _0^{\pi }\frac{r^2 \sin (\theta ) e^{-\lambda \sqrt{\rho ^2+r^2-2 \rho r \cos (\theta )}-2 r}}{\pi \epsilon ...
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2answers
209 views

How to make a single-variable out of a NDSolve solution?

So I've got this line that contains the solution of a partial, non-extraordinary differential equation (because Mathematica doesn't handle extraordinary partial differential equations): ...