Questions on the use of numerical functions NIntegrate and NDSolve.

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3
votes
1answer
88 views

Want NIntegrate to catch error message

Really stuck with this. When I use NIntegrate, it sometimes prints a message like NIntegrate::ncvb: "NIntegrate failed to converge to prescribed accuracy ...
3
votes
1answer
196 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
3
votes
2answers
176 views

NIntegrate returns zero for non zero integrand, 4d Integration

I am trying to calculate the following integral. ...
3
votes
1answer
2k views

Can Mathematica solve integro-differential equations?

I have integro-differential equations like this: ...
3
votes
1answer
705 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. ...
3
votes
1answer
203 views

Construct DifferentialMatrices and Kernel for LevinRule for this integral and ODE set

I've made a lot of progress on my problem the last few days thanks to all the help I've received on here. I think I'm upto the final step of greatly improving the performance of NIntegrate[..] on my ...
3
votes
1answer
529 views

Second Order Non Linear Differential Equation

I'm trying to solve the following differential equation numerically: ...
3
votes
0answers
54 views

Singularity treatment in a simple problem [duplicate]

With a simple search, several posts can be found on treating singularities encountered while using NDSolvefamily of numerical methods. However, most of them involve ...
3
votes
0answers
80 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 ...
3
votes
0answers
122 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. ...
3
votes
0answers
84 views

What am I missing in this highly oscillatory integral?

I want to numerically integrate this equation (in python without calling Mathematica): $\int_0^\infty {\rm d}k f(k) J_v(r k) J_n(s k)$ where $f(k)$ is a non-smooth function, $J_v$ are the Bessel ...
3
votes
0answers
302 views

Problem solving a nonlinear partial differential diffusion equation [closed]

EDIT: actualy the nonlinear partial differential equations for interacting density distributions, including boundary conditions, should be given as $$ \frac{\partial\phi}{\partial t} = D ...
3
votes
0answers
166 views

Numerical integration: complicated 2D integral seems to be poorly estimated

In the course of some physics research I've been working on, a very annoying integral has appeared that I'm having difficulty evaluating numerically. Any help you could offer would be greatly ...
3
votes
0answers
121 views

Nested NIntegrate of vector function

I am trying to perform a nested integration where the upper limit of the inner integral depends on the value of the outer integral, like in this question: Nested NIntegrate. Just like the linked ...
3
votes
0answers
314 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 ...
3
votes
0answers
1k 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: ...
3
votes
0answers
484 views

Numerically solving PDE with high precision

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 ...
3
votes
0answers
244 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
3
votes
0answers
1k views

Solving a system of nonlinear equations self-consistently

I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
2
votes
4answers
538 views

How to calculate this integral?

I am trying to Integrate the following Integral : $\int_1^{\infty } \dfrac{\left(x^2-1\right)^{13/2} e^{-ax} }{x^{10}} \, dx \,\, \,\,\,\,\,\,\,\,\,\,\,\,(a=\textrm{real>0})$ Mathematica didn't ...
2
votes
3answers
437 views

Solving an equation involving an integral

How do I get the following into Mathematica, solving for $a$: $$ 0.7 = 1 - \frac{2}{a} \times \left[ \frac{1}{a} \int_0^a \frac{x}{\exp(x)-1}\mathrm dx + \frac{a}{6} - 1\right] $$
2
votes
4answers
289 views
2
votes
2answers
1k views

optimization problem with NDSolve

I want to minimize the function fcc. When fcc is calculated for a specified point the answer is correct: ...
2
votes
3answers
388 views

How can I apply calculus to functions obtained from NDSolve?

Originally, I asked the question below, but the real underlying issue is as follows: When we solve an ODE numerically, I get the answer like this: ...
2
votes
2answers
225 views

FindFit working with Integrate but not NIntegrate - I am using “?NumericQ”

I'm having some syntax problems with finding a fit to an equation that doesn't have an analytical expression for it's integral. Because I think the problem is one of syntax, I am substituting a ...
2
votes
2answers
530 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 ...
2
votes
2answers
222 views

Attempting to use NDSolve to plot harmonic oscillator solutions

NDSolve[{ (-y''[r]/1880) + (470 (0.04077)^2 r^2 - 48 + 1/(1880 r^2)) y[r] == 0, y[0] = 0, y'[0] = 0}, y, {r, -4, 4}] I use this but get errors and am ...
2
votes
3answers
167 views

slwcon and eincr in integrating multivariate Gaussian random variables

Why is the following integration involving multivariate Gaussian distribution so slow and generating an error? Is there a better integration strategy? All that I'm doing is considering ...
2
votes
2answers
136 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 ...
2
votes
2answers
235 views

Plot result of non analytical-integral

I have the following function: h = 1; c = 1; k = 1; B2 = (2*h*c^2)/(x^5 (Exp[(h*c)/(x*k*T)] - 1)); (someone can see that this integral is the Planck function). ...
2
votes
2answers
552 views

How to compute this triple integral? [closed]

In Mathematica how can I compute this integral:$$ \iiint_{D}\sqrt{(1-9z^2)(1-4y^2-9z^2)}\,dx\,dy\,dz$$ where D is the domain: $$D: x^2 +4y^2+9z^2\le1$$ Please I need help!!!
2
votes
1answer
994 views

Optimizing a function involving NDSolve results in error messages

I want to minimize a function f with NMinimize but an error occurs that says: ...
2
votes
1answer
333 views

Syntax for integrating over limits specified by a Table

I wish to use NIntegrate to compute multidimensional integrals. However, I don't want to manually input the limits for the dimensions. I want to store the ...
2
votes
1answer
121 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 ...
2
votes
1answer
385 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 ...
2
votes
2answers
331 views

Perturbation theory with Mathematica: Definite integral of polynomial times exponential times hypergeometric function of imaginary argument

I would like to ask also Mathematica users about my question from the math forum. To expand, I'm adding the code which calculates the full double integral for $n=0$ and $\mu=0$ (the second in the ...
2
votes
1answer
206 views

Integration of a high oscillatory function

I want to get the numerical result of the integration below: ...
2
votes
2answers
180 views

NIntegrate - WorkingPrecision

I am trying to NIntegrate this expression. It is very close to zero, and so gives all possible types of errors. More precisely, ...
2
votes
2answers
89 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, ...
2
votes
2answers
92 views

numerical integration of equation obtained by ParametricNDSolve

I am trying to find a definite integral of the solution obtained using ParametricNDSolve (i.e. y[x,a,b]) from 0 to 1 and plot ...
2
votes
1answer
150 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
2answers
565 views

Wolfram Alpha will calculate this definite integral but Mathematica won't

I'm trying to compute a definite integral of the form $$\int_{0.2}^{0.5} \frac{1}{(1 - y)y^2\sqrt{0.5 - y^2 + y^3}}$$ in Mathematica. WolframAlpha will calculate this but Mathematica only outputs the ...
2
votes
1answer
330 views

Catastrophic loss of precision

I am trying to solve a double integral in the range of 0 to Infinity (for both the integrals) and Mathematica is giving me the following error: Catastrophic loss of precision in the global error ...
2
votes
1answer
293 views

2-Dimensional NFourierTransform

Mathematica FourierSeries package contains the NFourierTransform function for calculating 1-D Fourier integral numerically. ...
2
votes
1answer
388 views

Area between Contours in ContourPlot

I feel slightly foolish for asking this because I am so close, but I'm having trouble, so I will anyway. I asked this question two days ago regarding finding the lengths of contours. Now, I'd like to ...
2
votes
1answer
162 views

NIntegrate Warning / Error Messages

I am doing: NIntegrate[Sin[Exp[(x^4)]], {x, 2, Infinity}, PrecisionGoal -> 12] It prints out a host of warnings, but also shows the results as: ...
2
votes
1answer
802 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
333 views

Weighted mean of complex exponential function using NIntegrate

I have defined the following functions: ...
2
votes
1answer
797 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
2
votes
1answer
605 views

Creating hexahedral finite elements in Mathematica

Is it possible to do FEM using hexahedral elements in Mathematica? If it possible, is there any help to do that?