Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

0
votes
0answers
14 views

NDSolve : Solve a single variable-coefficient ODE as series of constant-coefficient ODEs

I have a manipulator equation of the form: $M(q){q''} + C(q,q')q'+G(q) = {0}$ where $M, C$ are $6$ x $6$ matrices, and $G, q$ are $6$ x $1$ vectors and $q$ a function of time. I would like to ...
6
votes
2answers
144 views

Reject diverging solution of NDSolve

I'm trying to numerically simulate a spring system with complex stiffness. In essence systems of the form $x''(t)+ (a+ ib) x(t)=0$ For this simple example an analytic solution is easy to find. The ...
13
votes
5answers
1k views

How do I obtain the enclosed area of this particular parametric plot?

I'm trying to find a way to obtain the enclosed area of this particular plot. Can someone show me how? ...
2
votes
1answer
51 views

Error accumulation in NDSolve?

I'm trying to solve this system of ODEs numerically: $$\vec{Q} = \vec{P} \times \vec{Q}$$ where vectors $\vec{P}, \vec{Q}$ have 3 components: $$\vec{Q} = \left( Q_1, Q_2, Q_3 \right) $$ $$\vec{P} = ...
2
votes
2answers
131 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
2answers
131 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 ...
8
votes
1answer
968 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 ...
2
votes
1answer
186 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
4
votes
1answer
60 views

WhenEvent used in a PDE to output independent variable

I want to use WhenEvent with a PDE after it has reached steady state. I'm posting a system of 2 equations (my real system has 6) and I'm solving the advection-diffusion-reaction 2nd order PDE. First ...
10
votes
2answers
197 views

How to use NDSolve with discontinuities at internal boundaries?

I don’t know how to impose discontinuous internal boundary conditions (BCs) in NDSolve, so I’ve set up an example problem to illustrate my issue. Consider the simple first-order ODE for $f(z)$ on the ...
2
votes
2answers
90 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 ...
10
votes
1answer
210 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. ...
0
votes
1answer
60 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 ...
0
votes
0answers
37 views

How to get this numerical solution of a integro-differential equation [migrated]

Previously, I ask an NDSolve questions(How to solve the differential equation with Duhamel's integral?), but now a more sophisticated one: ...
1
vote
1answer
90 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
1answer
36 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. ...
0
votes
0answers
60 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
94 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 ...
2
votes
0answers
87 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
1answer
88 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
87 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
1answer
73 views

Performing piecewise integration

The premise is that I am a new Mathematica user. I'm trying to evaluate the following ...
7
votes
3answers
199 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), ...
0
votes
0answers
55 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 ...
2
votes
1answer
158 views

How can I invoke the solution of NDSolve to determine a parameter in my equation just inside NDSlove?

I am trying to solve a differential equation by NDSlove for $h(x,t)$. It reads $$h_t=h_{xx}-V_h-\lambda(t)$$ where $V_h$ is a given function of $h(x,t)$ denoted by ...
0
votes
1answer
123 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 ...
10
votes
6answers
704 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 ...
0
votes
1answer
77 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: ...
14
votes
1answer
253 views
0
votes
0answers
47 views

NIntegrate unexpectedly returns complex number

I am attempting to visualise the effect of shift parameter $\gamma$ on the 3-parameter log-normal distribution. $$pdf(x;\mu,\sigma,\gamma) = ...
13
votes
1answer
2k views

What method does NDSolve use for solving PDEs?

What is NDSolve's mode of operation? I use it to solve partial differential equations and never gave it too much thought. Recently, I came across this question. ...
0
votes
2answers
53 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
2answers
115 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 ...
2
votes
1answer
87 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 ...
2
votes
0answers
47 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: ...
0
votes
0answers
28 views

Does a very large prefactor affect NIntegration time when plotting the result?

I'm using ListPlot[ NIntegrate[f[x,#],{x,a,b}]&/@Range[10,100] ] to plot the integral of the two variable function f as a ...
1
vote
0answers
35 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, ...
4
votes
1answer
456 views

Combining Gravity Turn and Orbit Models

I have a mathematical model for the motion of an orbiting spacecraft about Earth: ...
17
votes
4answers
2k views

Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 \leq 1$ in the first octant: ...
3
votes
2answers
562 views

Unexpected result of summation

I wrote a small module that gives me an incorrect output-set. It should be a single number! I don't understand what went wrong. This is the form of summation used: $$\frac{1}{2} (b-a) \sum_{i=1}^n ...
9
votes
2answers
353 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns ...
0
votes
1answer
77 views

Integral evaluation error

I have the following integral that I wish to evaluate using Mathematica: ...
0
votes
0answers
38 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 ...
3
votes
1answer
93 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] ...
0
votes
0answers
8 views

Numerical Integration with no lower limit [migrated]

Is there any 'natural' way to evaluate an integral numerically with a variable upper limit only? Actually I want to calculate the following residue $$\text{Residue}\left[\frac{z^3}{1-\pi ^4 z^4}\int ...
6
votes
0answers
94 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 ...
2
votes
2answers
86 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 ...