Questions on the use of numerical functions NIntegrate and NDSolve.

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0
votes
0answers
49 views

Ignoring Indeterminate Results [duplicate]

I am doing some program where I must calculate some numerical integral (the involved function is quite complicated to be solved analytically). The function to be integrated have some parameters which ...
-2
votes
1answer
370 views

Problem with plotting a function with NIntegrate

Why does the following Plot3D command never terminate? ...
6
votes
1answer
205 views

Specifying mesh in NDSolve

I am trying to solve a system of one-dimensional two-point boundary-value problems with NDSolve. I would like use a fixed mesh (specified by me) in the calculation. Is there a way to do this? The ...
0
votes
2answers
188 views

Is there a better way to approximate some graphs of integrals than interpolation?

I'm still pretty new to Mathematica so my apologies if this is a dumb question. I wanted to plot some integrals of functions for no particularly good reason, but the only decent way I could come up ...
1
vote
0answers
234 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
44
votes
3answers
1k views

When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: ...
0
votes
0answers
168 views

Integral of a transcendental equation

I have taken the following derivative of a transcendental equation using the D[...] function, as part of an approximation: ...
4
votes
2answers
272 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
3
votes
3answers
674 views

How to integrate a function over a 3D planar polygon?

I am trying to integrate a function over a planar polygon in 3D. In 2D, this is fairly straightforward, using either answer from this question (I use the second answer). If we use an equilateral ...
0
votes
1answer
180 views

Fast integration of 2D distribution across lines parallel to y-axis

I'm struggling with a small data set and a slow calculation. I have hundreds of small 2D data arrays and need to integrate across several lines parallel to the y-axis. Let me start with the data ...
0
votes
1answer
523 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
4
votes
2answers
726 views

Does Mathematica have a command analogous to ode45 of MATLAB?

Does anybody know if Mathematica has an analogue of MATLAB's ode45 command? I need to solve a second order coupled ODE system of equations.
3
votes
1answer
358 views

Multi-dimensional integral in the complex plane with poles and essential singularity

I've passed the last week searching a way to numerically integrate this multi-dimensional integral in the complex plane at the poles and avoiding the singularity at z=0: $$ \oint_{C}\oint_{C\ auound\ ...
0
votes
0answers
121 views

Integrating and plotting pde system solution

I have a trouble with plotting a pde system solution. I'm solving a PDE system in 2-dimensional space and then I want to integrate the solution along one dimension and build a log plot along the ...
1
vote
1answer
261 views

Simpson's rule with ListConvolve or ListCorrelate

I have a function that's represented as a long list of values that I want to integrate. I can do it procedurally with Simpson's rule. ListConvolve generally runs faster then procedural code, so i ...
9
votes
1answer
247 views

WhenEvent and partial derivatives

Can WhenEvent be used to reset the conditions on a PDE at a given time? How would the syntax of that be? This is the code I`m using ...
1
vote
1answer
216 views

NIntegrate converging too slowly when increasing size of array

I have a problem with a numerical integration. I have a 4x4x4x4 array that has for each entry an integral and I want to use NIntegrate to evaluate it. It gives me ...
6
votes
2answers
1k views

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 ...
2
votes
1answer
279 views

Numerical integration involving Inverse Normal CDF

I'd like to evaluate the following numerical integration using Mathematica $$ \ \int_0^T\int_0^\infty xe^{-0.04 s}g(x,s) dxds\ $$ where g(x,s) is a Gaussian copula function with say, marginal ...
8
votes
1answer
549 views

Integration strategies for oscillatory multidimensional function

I am seeking to integrate a highly oscillatory, multidimensional function. I am currently using NIntegrate's QuasiMonteCarlo approach. However, this is time-consuming and, given my current resources, ...
7
votes
1answer
353 views

Numerical contour integrations in the complex plane - contour deformation gives different answer for analytic kernel

I am trying to do a contour integration in Mathematica numerically. In particular, I'm checking the identity: $$ H_m^{(1)}(z) =\frac{i^{-m}}{\pi}\int_{-\pi/2 + i \infty}^{\pi/2 - i \infty} \exp[i m ...
0
votes
0answers
38 views

NIntegrate issue to do with unknown types [duplicate]

I have a numerical function zz: zz[s_ ? NumericQ] := so3toE3[Inverse[yn[s]].ND[yn[k], k, s]]; The other functions involved have 2 pages of code defining them so ...
3
votes
1answer
521 views

Monitoring the Evaluation of NDSolve: time to finish estimation

My problem is quite simple: I run a NDSolve with a system of many ODEs, a calculation that will run for many hours, and I would like to know the progress of the ...
7
votes
1answer
668 views

Determining which rule NIntegrate selects automatically

I need to numerically integrate a highly oscillatory function over the semi-infinite domain $(0,\infty)$: $$\int_0^\infty \frac{\sin^2(x) \sin^2(1000 x)}{x^{5/2}}\mathrm dx$$ Since the Levin rule ...
0
votes
0answers
174 views

Function not recognized by Mathematica?

I'm trying to do triple integration on a bivariate function where one of the upper integration limits is the variable of the outer-most integration. When I execute the following lines, Mathematica ...
1
vote
0answers
329 views

Cauchy principal value integral of a list of numbers. How?

I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
1
vote
0answers
791 views

NDSolve: methods and step size choosing

I am looking into the documentation of NDSolve[]; more precisely how this function chooses the StepSize and how it chooses which ...
1
vote
1answer
135 views

Double integral 0

I am trying to reproduce the results from a paper in Mathematica. This task involves $K$ double integrals of the form $$\int f(x,y)g(x)dx,$$ where $f(x,y)$ is a bivariate normal density with mean ...
5
votes
0answers
120 views

Numerical solution of Schrödinger-type equation in Mathematica [duplicate]

I want to solve the following differential equation numerically: \begin{equation} i\partial_{t}\psi(r,t)=\left[-\frac{\Delta}{2m}+g\left|\psi(r,t)\right|^{2}+V_{d}(r,t)\right]\psi(r,t) \end{equation} ...
18
votes
4answers
841 views

How to calculate the volume of a convex hull?

Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
2
votes
2answers
312 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
3
votes
0answers
607 views

Using NDSolve for Integro-Differential Equations

I have a fairly complicated set of coupled non-linear integro-differential equations that I am trying to solve using NDSolve. The equations are: ...
2
votes
1answer
359 views

NDSolve with vector function

(Possible duplicate yet I still can't understand.) Basic 2D revolving around origin: ...
5
votes
1answer
379 views

Solving homogeneous Fredholm Equation of the second kind

I am trying to solve a homogeneous Fredholm integral equation of the second kind, i.e. $\lambda y(x) = \int\limits_a^b e^{i[\phi(t)+k(t-x/M)^2]} y(t)\,dt$ where $\lambda$ is the eigenvalue (to be ...
5
votes
2answers
700 views

How to deal with zero in NDSolve in mathematica?

I would like to solve the following ODEs $$\begin{cases} x'(t)&=y\\ y'(t)&=-y(t)/t-e^{x(t)},\\ x(0)&=1,\\y(0)&=0, \end{cases}$$ (EDIT : The second equation used to be $y'(t) = ...
2
votes
1answer
465 views

Getting MemoryAllocationFailure from NIntegrate

When numerically calculating a double integral using NIntegrate over an infinite domain (with all options at their default), Mathematica 7 calculates my integral ...
2
votes
0answers
39 views

NIntegrate/NSum with parameters [duplicate]

I'm trying to calculate a continuous integral within a discrete integral. Something similar to this (yet more complex): ...
1
vote
1answer
413 views

NDSolve diffusion equation over/underdetermined

I have a feeling the solution to my problem is very simple… but my knowledge of differential equations is pretty weak. I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
0
votes
1answer
221 views

DAE - varying initial conditions

I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here: Putting NDSolve into ParametricPlot But it does not work: ...
18
votes
2answers
866 views

3D orbits and inaccuracy over time

I wrote a little program to use Newton's Law of Universal Gravitation to animate 3 planets orbiting a central star, but I have run into a problem. Here is the code that I used to create the program (I ...
2
votes
1answer
396 views

How to adjust parameters to experimental data on a NDSolve problem

I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3. ...
7
votes
0answers
426 views

Numerically solve 2nd order differential equation with singularity

Consider a second order differential equation with a potential that diverges at some generic value in the variable. For example: $$-y^{\prime\prime}(s)+\frac1{\mathrm{cn}{(s\mid k^2)}}y(s)=0$$ where ...
5
votes
1answer
129 views
9
votes
1answer
466 views

Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?

I am trying to evaluate this integral numerically $$ \int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q $$ for large values of $R$. This makes the integrand oscillate more quickly and Mathematica ...
3
votes
1answer
819 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: ...
2
votes
0answers
249 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 ...
0
votes
1answer
133 views

Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
1
vote
0answers
263 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
419 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...