Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

3
votes
2answers
122 views

How should I tweak the options in NIntegrate?

I'm trying to obtain an accurate result from a difficult-to-integrate function and I've thrown in the kitchen sink worth of options in NIntegrate. I think I'm ...
0
votes
1answer
79 views

Calculation Performance (slow Plotting)

I have a functions, which is an Integral. It is exaclty this function Zf[x_] := 2*I*NIntegrate[Exp[-y^2.0 + 2.0*I*y*x], {y, 0, Infinity}]; Later I need to plot a ...
2
votes
1answer
47 views

Integrate and NIntegrate combined, giving MaxPrecision error

I am trying to integrate the following : ...
14
votes
1answer
422 views

How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area. The function ListSurfacePlot3D creates the surface how I want it. ...
-2
votes
1answer
46 views

NIntegrate a function containing NDSolve

I am having an issue integrating a function for which I am getting values for when I evaluate it. ...
1
vote
1answer
96 views

How do I solve this ODE numerically in Mathematica?

I want to solve these equations numerically in Mathematica and plot them. \begin{equation} u'(t)=1.5\,u(t)\,v(t)-u(t) \space \space \space \text{and} \space \space u(0)=0.001 \end{equation} ...
2
votes
0answers
116 views

Different solutions for seemingly same Integral

I want to evaluate the following integral: $$\int_{\left(1-\sqrt{a}\right)^{2}}^{\left(1+\sqrt{a}\right)^{2}} \frac{1}{2\pi ...
0
votes
0answers
63 views

Finding when a ODE returns to starting position

I am trying to discover when these ODE return to their start position. I am using coordinates that have a periodicity of {Pi/2, 2Pi, 2Pi}. To accomplish this I have had to use mod. The ODE are ...
0
votes
0answers
132 views

How to optimize a cost function which involve the solution of a ODE system using the NMinmize?

I have created a cost function, the value of which depends on the solution of a ODE (ordinary differential equation). The parameters of the ODE are not determined, and my goal is to determine them ...
0
votes
0answers
112 views

Integrating a highly oscillatory function

I am trying to numerically evaluate the integral $\int_{-\pi}^{\pi}\mathrm{d}x f(x) \mathrm{e}^{\mathrm{i} xn}$, where $n$ is a large number, say 50. The errors I get are NIntegrate::slwcon and ...
0
votes
0answers
83 views

Improve the speed of Gaussian quadrature integration

I am using Gaussian quadrature method to do numerical integration for a function Pderivative, which is related to the demagnetization tensor of ...
1
vote
1answer
86 views

Performing piecewise integration

The premise is that I am a new Mathematica user. I'm trying to evaluate the following ...
5
votes
1answer
342 views

Why does DSolve give a different result than NDSolve?

When I try DSolve to solve a system: ...
0
votes
1answer
274 views

Numerical integration converging too slowly

I must solve this integral which I suppose to be a very small number. How can I do? When I wrote this code: ...
8
votes
3answers
289 views

NIntegrate of surface area of intersecting spheres yields zero

I have a bunch of spheres (it's actually diamond cubic structure. The 0.6 radius doesn't matter), ...
2
votes
0answers
55 views

Better to have infinities in limits or integrands (`NIntegrate`)? [closed]

I'm using ListPlot to plot the integral of a function with respect of the function's second variable: ...
2
votes
1answer
155 views

Numerically integrate and plot $f(x;p)$ for a range of the parameter $p$

Suppose we have an integral of the form $$I = \int_a^b dx \, \sin(px), \tag{1}$$ where I've take $f(x;p) = \sin (px)$ to be specific. I want to plot this integral for a range of values of the ...
7
votes
2answers
389 views

How much time should one give Mathematica for an integral evaluation?

Sometimes when I do integrals in Mathematica (M), it keeps thinking and thinking and I have no idea what is going on inside M. For how long should one wait or how does one know whether M has not got ...
1
vote
0answers
42 views

Which type of integrals are better for Mathematica [closed]

Is it in general better to type in a integral with its limits, or is it better to type an indefinite integral into Mathematica? With better I mean: Likelihood that Mathematica can solve it, ...
0
votes
0answers
60 views

Improve speed in module with NIntegrate and FindRoots

I am running version 10.1 in Windows 7. The following code gives good results but I have two questions: Is there a way to speed up the program as I would like to compute more data points? The code ...
0
votes
1answer
96 views

Integral evaluation error

I have the following integral that I wish to evaluate using Mathematica: ...
2
votes
2answers
144 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 ...
0
votes
0answers
54 views

Problem with plotting a piecewise function [duplicate]

I'm having a very puzzling issue with piecewise defined but smoothly continuous functions. I have a perfectly continuous piecewise function defined as ...
10
votes
6answers
820 views

Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
8
votes
2answers
535 views

How to solve the differential equation with Duhamel's integral?

How do I solve a differential equation with Duhamel's integral? I tried to solve it with NDSolve, but failed: ...
1
vote
1answer
79 views

Assymptotically Solving ODE with free parameters

I have a first order ODE, $F(y[x], y'[x], A, B) = 0$. I want to solve this numerically (with the boundary value $y[1] = i$ ) but also with the following requirements: A and B are free parameters which ...
0
votes
0answers
71 views

NIntegrate fails to converge around a value out of integration range

This is the function that I am trying to integrate, I have interpolated it for best results (would rather not): There is a 'singularity' around 0, but I get the warnings and bad results even when ...
0
votes
0answers
54 views

Integration problem: lrgexp

I want to calculate the following integration but it gives the error PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD. The code is: ...
2
votes
1answer
446 views

Plotting NIntegrate

Plot[E^(-0.5 x) NIntegrate[Cos[t] E^(Cos[t] + 0.5 t), {t, 0, x}], {x, 0, 40}] Mathematica evaluates this integral for each point, which takes a long time. It is ...
8
votes
1answer
265 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
0
votes
0answers
130 views
0
votes
1answer
96 views

Numerical integral speed

I have the following code to calculate a numerical integral for any given a, however it takes a very long time, even with adaptivemontecarlo, which is not accurate enough: ...
19
votes
4answers
920 views

A bug in Integrate

Integrate[(1 + 16 Tan[2 x - y]^2)/(1 + 4 Tan[2 x - y]^2), {x, 0, 2 π}] Mathematica (wrong) output is (tested under versions 8 and 10.0, took ~ 1 minute of CPU ...
8
votes
2answers
280 views

Why does Mathematica say $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$?

Mathematica 9 says that $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$ and $\int_0^1\int_0^1\int_0^1\frac{1}{xyz}\,dz\,dy\,dx=0$. ...
2
votes
1answer
174 views

Solving an integral equation numerically

my problem is: I get the result of definite integral and now I need to find the upper limit for the same integral but with opposite sign value so f2=-f1. ...
0
votes
2answers
327 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
0
votes
0answers
70 views

Integration is unevaluated analytically after a variable removed

I am using Mathematica 9.0 to do a symbolic integration as follows: ...
-1
votes
1answer
137 views
2
votes
0answers
151 views

The idea behind Stiffness switching method with NDsolve [closed]

Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?
1
vote
2answers
131 views

Integral too oscillatory

Is there any way top make this integral less oscillatory? ...
4
votes
1answer
116 views

Kernel crash when using NIntegrate with Throw/Catch

Bug fixed in 10.2.0 My code is: ...
0
votes
1answer
283 views

How to do multiple integral numerically?

I cannot calculate the following type of integrals numerically : $\int_0^1 dy \int_0^y f(x) dx $ $f(x)$ can be a complicated function. The problem is due to the fact that the upper limit of one of ...
2
votes
2answers
175 views

Approximation of definite integral by parabolas

This question is related to Trapezoid approximation to definite integral. As promised, I am now asking about how to draw approximation of integrals by parabolas. I tried to modify MarcoB's code, and I ...
-2
votes
1answer
143 views
2
votes
1answer
68 views

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function?

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function waited to be solved by NDSolve first? For example, ...
2
votes
1answer
102 views

Why isn't Table iterator value inserted in failed NIntegrate arguments?

Consider this simplest example: Table[{z, NIntegrate[f[x], {x, 0, z}]}, {z, {1}}] Here f is not defined, so ...
8
votes
2answers
341 views

What's wrong with NIntegrate with “MonteCarlo” Method?

Bug fixed in version 10.2.0 My code is: ...
6
votes
2answers
202 views

Why does Nintegrate keep unevaluated?

Bug introduced in 10.0 and fixed in 10.2.0 It's no surprise that the "MonteCarlo" Method works well: ...
0
votes
2answers
71 views

NIntegrate fails when integrating over a list from an external (MathLink) function

NIntegrate fails when integrating over a list from an external (MathLink) function. For simplicity, consider an external function f[x] that returns the list {x,2x}. In Mathematica, the function would ...
3
votes
3answers
273 views

NIntegrate-ing a compiled function

I'm trying to integrate numerically in 6 dimensions a very long expression and I read about the option to NIntegrate a compiled function which should be faster. ...