# Questions tagged [numerical-integration]

Questions on the use of numerical functions NIntegrate and NDSolve.

363 questions with no upvoted or accepted answers
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### Solving the 2D Schrödinger equation with eigensystem, then verifying orthonormality of eigenfunctions with NIntegrate

I am solving the time-independent 2D Schrödinger equation for an interacting electron and hole in the case of anisotropic electron and hole masses, where the interaction is described a modified form ...
337 views

### Spurious Error Messages from NDSolve when Using WhenEvent with Time Delays

Bug introduced between versions 10.1 and 10.4, and resolved in 11.3. Using either 11.2 or 10.4 on Windows 10 (64 bit), I am unable to reproduce the answer by March to question 99576. Specifically, ...
102 views

### Bug in integral related to beta distribution

I've encountered a problem, which I'm pretty sure is a bug. I've contacted Wolfram's support and they were less than helpful. I'd like to bring the issue up here to get either a confirmation that it ...
364 views

### Integrating rational functions of several variables over $\mathbb{H}^4$

Let $W$ be a rational function of $8$ variables $a,b,c,d,e,f,g,h$ from this file, e.g.: ...
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### Modelling Hysteresis with a Differential Equation

I want to implement the bulk ferromagnetic hysteresis model (mostly the Jiles-Atherton Model), see http://drum.lib.umd.edu/bitstream/1903/6043/1/PhD_99-1.pdf page 44 equation (30). The needed ...
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### Solve integral equation for upper bound

I need to find the upper bound of an integral knowing the value of the lower bound and the result of the integral. Here is my function: f[t_] = Sqrt[1 + E^(-2 t)] ...
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### How can I do a faster integration?

I have this part of my code, which takes forever to run. Does anybody know how to make it faster? Using NIntegrate I face error: "NIntegrate::eincr: The global error of the strategy GlobalAdaptive ...
252 views

### System of coupled PDEs: “Repeated convergence test failure” error

I am trying to solve the following system of coupled PDEs but I am getting an error. ...
43 views

### Determine the method that has been used for numerical solution of elliptical PDEs

I am using the following script to solve a system of PDEs: ...
80 views

### Extract explicit region (integration bounds) from ImplicitRegion

Using an ImplicitRegion in NIntegrate by far best performance is obtained by using ...
132 views

### Unexpected Behavior of Parametric Sensitivity in ParametricNDSolveValue

Bug introduced in 10.4 or earlier and continuing through 11.3 Submitted as CASE:3916971 While exploring alternative methods of solving 33538, I encountered difficulties with the parametric ...
109 views

### Improve accuracy of NIntegrate with GlobalAdaptive over ImplicitRegion?

Let's say that I want to integrate some arbitrarily "nice" function (uniformly $C^{\infty}$-smooth, for example) over an ImplicitRegion in more than three dimensions. For example, let's consider the ...
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### worst performance in numerical integration in ver. 11.1

I would like to know if anyone of you have experienced slow down performance in numerical integration. I have tested this code in ver. 11 and ver. 11.1: ...
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### “ParallelDo” does not calculate the function well

Now, I'm solving utility maximization problem. ...
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### Building integrators and how they compare across platforms

I'm interested in building some numerical integrators. Specifically symplectic integrators. Now, my Mathematica has been coming along, day by day, slowly but surely. Still not at a stage where I can ...
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### How can one achieve the most accurate estimates of certain six-dimensional integrals under specific constraints?

I have three positivity constraints (f1, f2, f3): ...
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### Integrate gives wrong result?

Computing the integral of the Euclidian distance of two points in a plane, Mathematica seems to give a wrong result. This is a simple integral that should not be tricky and can easily be computed by ...
164 views

### Help on using NIntegrate Method -> {Automatic, “SymbolicProcessing” -> 0}

I'm trying to take an integral of a super oscillatory function as follows. It takes a long time to solve it with the NIntegrate so I added the option ...
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### Integration error from Plot3D

I am trying to visualize diffusion distribution from an equilateral triangle with 45 degrees. Assuming that diffusion is a Gaussian with sigma=1 this should do: <...
664 views

### Implementing the Numerov method for solving ODEs with NDSolve

I'd like to implement the Numerov scheme for solving an ODE (Scroedinger Eq time-independent) with NDSolve. I tried in analogy with the Runge Kutta example in the ...
268 views

### NSolve doesn't work on an equation containing a numerical integral and constraints

I'm having trouble getting Mathematica to solve equations numerically. I know that its important to specify the type of variables for pattern testing (see e.g. here) but this doesn't seem to work. ...
705 views

### NDSolve fixed step problem

Working example here: Drive folder (have both files in the same directory! Notice: the line <<variables' in the file seems to throw an error for me, but ...
438 views

### Function with a sharp resonance which Mathematica fails to integrate. Why?

I'm a new user of Mathematica and I'm trying to use it to calculate the collisional cross-section as a function of energy for a given potential and decay rate. I know that the resulting function ...
623 views

### Global vs local adaptive integration: lattice propagator

I was doing the first exercise in the paper Lattice QCD for Novices. This is the expected result: With the default "GlobalAdaptive" method for NIntegrate it threw errors saying that the error had ...
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### ParametricNDSolve and ProcessEquations

I have a question regarding NDSolve`ProcessEquations and ParametricNDSolve. When using the regular NDSolve we have the option to divide the integration into the three steps ProcessEquations, Iterate ...
I want to numerically solve the PDE $\partial_t u(t,x)=c\partial_x u(t,x)+(mx-l)u(t,x)$ with some initial and boundary conditions and given parameters $c$, $m$ and $l$. Consider the code ...