Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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1answer
45 views

NDSolve with coupled ODE's and unknown singularities

I have two coupled ODEs that I am trying to solve numerically. It appears that there is a singularity in the solution to the equations which I am unsure how to get past. Both functions $\alpha$ and ...
12
votes
1answer
72 views

Empty WhenEvent action crashes kernel

Bug introduced in 9.0 and persisting through 10.4.1 WhenEvent is new in 9.0. This is an example from the docs, slightly modified (action is wrapped in ...
2
votes
0answers
92 views

Mathematica Newmark Optimization

Here is my Mathematica code which implements the Newmark method to solve a equation of motion. The variable "ag" contains the accelerations from an earthquake record. Is it possible to optimize this ...
0
votes
0answers
75 views

Why Integral does not converge?

I am trying to solve for $\Omega$ this nonlinear integral equation : $$1+\dfrac{z}{k^2}-\dfrac{z^2}{K_2(z)} \dfrac{\Omega}{k^3} \displaystyle\int_{1}^{\infty} \gamma^2\, \text{ArcTanh} ...
0
votes
0answers
41 views

NDSolve kernel crash, affected by variable naming

The following isolated example cannot be further simplified much to reproduce a crash. I've already submitted the issue to TechSupport, but it seems this is not an easily reproducible case, so I'm ...
2
votes
1answer
64 views

Does NDSolve iterate faster in a region where the system being solved is in equilibrium?

I was wondering how exactly the time it takes for NDSolve to iterate through a certain region of the domain depends on the local behaviour of the given system being solved. My guess would be the ...
0
votes
0answers
63 views

Force NDSolve to use finite difference

How to force NDSolve to use finite difference instead of FEM. I have the following code: ...
0
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0answers
70 views

Boundary conditions for NDSolve

I get the following message: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >> from ...
11
votes
1answer
203 views

NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
4
votes
1answer
66 views

Issues with modeling pulses in a very simple system of DAEs

Some time ago I had asked this question about evaluation difficulties using Euler Integration to solve a system of ODE where discrete pulses occur. While I have now abandoned Euler integration and ...
1
vote
2answers
103 views

Numerical integration does excessive coarse-graining?

I am trying to perform numerically the following integral $$\int_0^8\text{d}x\,\text{Re}\left[\frac{e^{-\frac{a^2}{2}-\frac{x^2}{2}} x^4 \sin (b x)\left(e^{-i c x} \text{erfc}\left(\frac{-c +i x ...
-1
votes
0answers
75 views

Integral Equation Solving [closed]

I need to solve two coupled equations such as ...
0
votes
0answers
27 views

Take a derivative of a NIntegrate function (with two argument) [closed]

what I have is a numerical function of SBE[m,T] and I want its derivative with respect to T. Here is what I wrote, ...
3
votes
2answers
89 views

Switching Differential Equation in NDSolve

I am trying to solve the following system of differential equations using NDSolve: $\dot{z}_t=.5(1-z_t)$ $\dot{y}_t=.05y_t+z_t-x_t$ subject to the following constraint: $-y_t-z_t\le0$ where $z_t$ ...
10
votes
1answer
190 views

NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer

After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ...
1
vote
1answer
82 views

NIntegrate gives two results for two forms of the same function. Which one to trust?

I am interested in evaluation the following integral numerically (since apparently there is no analytical solution) $$\int dx \,x^3 \left(e^{2 i c x }-i \text{erfi}\left(\frac{x +i c ...
0
votes
3answers
81 views

Average function value over an Interval [closed]

What is the best way to find the average value of a function over a specific interval in Mathematica? I can not figure it out. I have two points on the interval and need to find the average value.
1
vote
1answer
201 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
5
votes
1answer
125 views

Multiply integrand with -1, and the precision changes?

"After multiplying the integrand of NIntegrate with -1, the Precision of the output will ...
18
votes
1answer
464 views

Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
-3
votes
1answer
35 views

Method to compute NIntegral of Trigonometric functions

I don't know which method to adopt for computation of the following integrand on the unit sphere in $R^6$: $ 2 r^9 \sin ^5(\text{$\theta $1}) \sin ^3(\text{$\theta $2}) \sin2(\text{$\theta $3}) \sin ...
8
votes
2answers
132 views

How to improve accuracy of NIntegrate over ImplicitRegion

I'm trying to compute the area of a implicit region given as ...
14
votes
2answers
239 views

What can one do with extremely stiff problem in NDSolve?

Consider the following illustrative problem: $$ \frac {\partial f} {\partial t} = \frac {\partial} {\partial x}(x f) + \frac {\partial} {\partial x}(f \frac {\partial f} {\partial x}) $$ This is ...
3
votes
1answer
45 views

Performance of numerical integral over piecewise function

Using mathematica version 10.3, I observe that an integral over a piecewise function evaluates a factor 10 slower than the same integral without the piecewise distinction. Here is the code: ...
1
vote
1answer
42 views

Using NIntegrate on a joint CDF without getting an error

I am trying to calculate the area under a constrained part of a function built from the empirical CDFs of two distributions. When I calculate the area of either CDF using NIntegrate it works fine, ...
0
votes
0answers
32 views

Stable numeric integration of multidimensional step function

I am trying to integrate numerically a two-dimensional function (a SmoothKernelDistribution) with a step. I tried a few different settings for the parameters of ...
0
votes
1answer
91 views

How to omit the corrupt value in a program?

I've such errors: Coordinate .. is not a floating-point number and can't correctly fix it. The problem occures when x==Log[2] The program works correctly ...
2
votes
1answer
114 views

Differential Equation with Numerically Integrated Boundary Conditions

I have a second order differential equation that I'd like to solve numerically, and then integrate its solution twice to get the parametric equations of a curve. The ODE is: $2 ...
1
vote
0answers
52 views

How to do numerical line integral?

I have a 2D numeric (interpolating) function J that represents the current density of a square plate. I'd like to integrate J along one edge to find the total current coming out of that side. I'm ...
1
vote
1answer
51 views

AbsoluteTiming of nested integration gives strange result

I found somewhat strange behaviour of nested integration timings. Consider the following code: ...
1
vote
1answer
45 views

Getting an error with NIntegrate due to insufficient WorkingPrecision or divergent integral

Hello I have the following problem. But when I try to solve it, I get an error saying 'Catastrophic loss of precision in the global error estimate due to \ insufficient WorkingPrecision or divergent ...
2
votes
0answers
56 views
0
votes
1answer
71 views

NDSolve for a system of nonlinear coupled pde

I try to solve a system($n$) of coupled nonlinear 1-d PDE's which is basically coupled sine-Gordon equations (through 2nd spatial derivative) in time and space. I am interested in the dynamics when I ...
0
votes
0answers
23 views

Optimizing NMinimization and NIntegration with a Nested List-Valued Function

I want to use NMinimize and NIntegrate on each element of a nested list-valued function. Here's a simple example of what I'm ...
1
vote
1answer
69 views

Numerical integration plot

I am trying to do a numerical integration plot in Mathematica. Specifically, I want to plot $r$ versus $\tau$ where, $$\frac{dr}{d\tau}=\sqrt{2F(r)}$$ $F$ being a quartic polynomial. The limit of $r$ ...
0
votes
1answer
86 views

difficulty in numerical estimate of double integral

I entered the following simple integral in mathematica: ...
0
votes
1answer
64 views

Why does Mathematica 10.3.1 fail me on : Integrate[(x^3) [Log[2 Sin[x]]]^8, {x, 0, Pi}] [closed]

All it gives me is a pretty restatement of my original request. When I use WolframAlpha PRO, I get a result of 624510 and a visual representation of the area in question. I know the ends of the ...
10
votes
0answers
131 views

Strange behaviour of integrals with Cos, Sin, and Exp

During the study of the problem How to solve this integration? I have discovered a strange behaviour of some integrals. I would consider it a bug. ...
4
votes
3answers
186 views

How to solve this integration? [closed]

I need to find the integration of the following expression ...
1
vote
1answer
66 views

numerical integration over divergence

Consider the following function g1: ...
2
votes
1answer
126 views

The numerical solution of a nonlinear ODE: boundary value problem

I want to solve the following nonlinear ordinary differential equation with boundary values $f(0)=1$ and $f(1)=1$: $${\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}f \left( x \right) ={\dfrac { \left( 51-51\,x ...
3
votes
3answers
63 views

Replace variable with value prior to evaluating NIntegrate

The title says it all. Reading posts such as this however, I'm not seeing how to do this. This is the simplest example that can show my problem. ...
2
votes
1answer
45 views

Numerical Integration with absolute value [duplicate]

I want to find the area enclosed by the fourth heart curve (http://www.wolframalpha.com/input/?i=fourth+heart+curve). Since both $y(t)$ and $x(t)$ are given and I know that $t$ is in the range ...
0
votes
0answers
59 views

Another question about inverse Laplace transform

Given $r = 0.06;\quad \theta = 105;\quad \kappa = 1;\quad x_0 = 100;\quad K = 100;\quad \sigma = 0.10;\quad T = 0.25;$ Define $ \nu = -\kappa/\sigma^2 - 0.5;\quad p = \kappa*\theta/\sigma;\quad q = ...
0
votes
0answers
23 views

Nested Numerical Integration [duplicate]

So I am trying to evalute the following Integral Numerically: $$\int_{\mathcal{J}^+(x_0)\cap\mathcal{J}^-(x_f)}^{}A(x_0,x_1)\int_{\mathcal{J}^+(x_1)\cap\mathcal{J}^-(x_f)}^{}A(x_1,x_2) dx_1dx_2$$ ...
2
votes
2answers
91 views

How to find the integrand singularity points when having NIntegrate::slwcon:

In order to calculate the closed area of the curve below defined by parametric equation curve02, ...
3
votes
1answer
44 views

My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
0
votes
1answer
45 views

ND on a function using NIntegrate

I need to numerically differentiate a function that takes a list as an argument and that uses NIntegrate in its definition. A simple example is ...
1
vote
0answers
40 views

Numerical Integral with Boolean as part of argument

I am trying to numerically calculate a partial surface area integral of an oblate spheroid in spherical coordinates. The area I want to calculate is determined by a boolean function in the argument of ...