Questions on the use of numerical functions NIntegrate and NDSolve.

learn more… | top users | synonyms

2
votes
1answer
197 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
63 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
210 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 ...
3
votes
2answers
98 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 ...
12
votes
1answer
280 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
61 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 ...
1
vote
1answer
92 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
38 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
61 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
102 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
90 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
93 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 ...
7
votes
3answers
210 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
61 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 ...
0
votes
1answer
84 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
254 views
0
votes
0answers
49 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
56 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
122 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
97 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
48 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
38 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
518 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
585 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
368 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
81 views

Integral evaluation error

I have the following integral that I wish to evaluate using Mathematica: ...
0
votes
0answers
41 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
101 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] ...
6
votes
0answers
100 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
93 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
50 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 ...
7
votes
2answers
300 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: ...
4
votes
2answers
1k views

How to plot and solve the numerical solution of a integro-differential equation

I have a integro-differential equation of the form $y'(t) = - \int_0^t {y(t_1 )} e^{t_1 - t} dt_1, {\rm{ t}} \in {\rm{[0,10], y(0) = 1}}$ My code is: ...
3
votes
0answers
52 views

Using indexed array elements as integration dummy variables with EvaluationMonitor. Bug?

As part of a routine that must cope with integration of varying numbers of dimensions, I would like to use indexed variable names (e.g., x[0], x[1],...) as dummy integration variables. However, it ...
1
vote
1answer
64 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
41 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
39 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: ...
1
vote
2answers
81 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 ...
3
votes
1answer
238 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 ...
2
votes
1answer
535 views

Use Euler method to solve differential equation

Use Euler's Method or the Modified Euler's to solve the differential equation ${dy/dt=y^2+t^2-1, y(-2)=-2}$ on $[- 2, 2]$. Take h = 0.2 (...
2
votes
2answers
444 views

Plotting several numerical solutions plus the analytic solution of ODE in one plot

I want to be able to plot several numerical solutions of an ODE, plus its analytical solution in one plot, in order to see how the numerical solutions converge towards the analytical one with respect ...
1
vote
1answer
909 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: ...
5
votes
1answer
645 views

NestList and Euler's method

I am new to mathematica and so just experimenting with various programming constructs. Recently have been looking at NestList and how I could use this to implement ...
3
votes
1answer
107 views

Precision of NIntegrate

At the moment I am considering a "difficult", highly-oscillatory integral in Mathematica. It calculates the integral without any complaints. However, I am also trying out a numerical method with which ...
1
vote
2answers
85 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 ...