Questions on the use of numerical functions NIntegrate and NDSolve.
2
votes
0answers
20 views
Monitoring time step manually within RandomFunction
Consider the following stochastic differential equation
...
0
votes
1answer
67 views
Solving self-consistent equation that involve using NIntegrate [on hold]
I am trying to solve numerically in Mathematica self-consistent equation that I have as:
NSolve[s == 1 + f[x, y, z, s, 10], s, Reals]
where ...
0
votes
2answers
82 views
Integrals of a Fourth order differential equation: Part B
I want to continue this topics (enter link description here):
Is it possible for us to get the value for integrals of a Fourth order differential equation (But) which includes a constant parameter?
...
0
votes
2answers
60 views
Integrals of a Fourth order differential equation: Part A
Is it possible for us to get the value for integrals of a Fourth order differential equation in MMA.
I attach the code that i have used in MMA:
...
1
vote
3answers
53 views
NDSolve output as input to another NDSolve
I want NDSolve to solve the problem $$y'(x)=0, y(0)=1, x\in[0,1] $$ and then use $y(x)$ to solve $$z'(x)=y(x), z(0)=0, x\in[0,1] $$.
This is a toy model of the real problem.
In the real problem ...
-4
votes
1answer
80 views
A difficult problem about the “FindRoot”
I use the parameters to calculate the Φ in the final, but I don't know what happen, it shows a lot of information, but I can't understand. I am using this code to solve the problem. This code is ...
0
votes
1answer
55 views
Numerical solution of differential equation with boundary condition at infinity
I have the following ODE for a function $F(x)$: $F''-\frac{1}{x}F'-aF=0$ with the following boundary conditions: $F(x\to0) = 1$, $F(x\to\infty)=0$. It can be solved analytically: $F = \sqrt{a}xK_1(\...
0
votes
0answers
65 views
Plot a function with very small values, close to zero
I want to plot a function with very small values, close to zero, but even though the limit is -3/2 as x->0, I can't get any ...
1
vote
3answers
59 views
Sum of all the n-th numerical evaluation of an integral and its cumulative sum of the square of the n-th value
I wish to compute the expansion coefficient of a wavefunction(i.e. in quantum mechanics) which in itself is an integral, given by
$$b_{n00} = \int^{\infty}_{u = 0} \frac{1}{(n)^{3/2}} L^{1}_{n-1}\left(...
0
votes
1answer
62 views
Find Root doesn't work properly
I use a FindRoot that doesn't find the right solution in some range, the FindRoot is the following:
...
0
votes
1answer
53 views
How can I solve this BVP using mathematica?
I need to solve the following BVP:
$$(g^{-1/3}f'')'+ff''=0$$
$$(g^{-1/3}g')'+0.71fg'=-1.43775g^{-1/3}(f'')^2$$
With the following constraints:
$$f[0]=0,f'[0]=0,f'[20]=1,g[0]=0.944175,g[20]=1$$
I used ...
0
votes
1answer
45 views
How can I compute the derivative of a variable after it is solved using NDSolve?
I have a 4th-order(with respect to x and 2nd-order with respect to t) pde which is solved easily using NDSolve for the variable v[x,t]. Now, I also want the value of 3rd-order partial derivative of v[...
1
vote
1answer
76 views
Stability of the numerical methods for SDE
I've been figuring out with the methods for integrating of stochastic differential equations in Mathematica. I've considered the one-dimensional system:
$$dx=-x dt+\sigma x dw$$
with some initial ...
-1
votes
1answer
69 views
nlnum problem of NDSolve
I'm having a difficulty to NDSolve a ODE due to nlnum (according to the error message). Below is the code I have. First of all are functions:
...
1
vote
2answers
67 views
Solving an ODE with a sign/step function which depends on the time derivative
I'm trying to solve a set of ODEs with a Heaviside step function which depends on the sign of the derivative of the function.
This is a simplifying example of what I'm trying to do
...
0
votes
1answer
35 views
problem with integration and plot
I have a problem with the following function, I want to integrate my function on r for r between 0 and infinity and then plot it, but I can't compute it, I get the following error...
Integrate::...
0
votes
0answers
60 views
1
vote
1answer
49 views
-1
votes
1answer
83 views
Getting errors NIntegrate::nlim and NIntegrate::slwcon [closed]
Here is the modified question:
First: Define
phi[x_]:=Piecewise[{{1, 0 <= x < 1}}, 0]
...
0
votes
0answers
50 views
Problem with NIntegrate: it gets stuck when evaluating zero value
I have an integral with complicated function evaluated by MonteCarlo method (please find a folder with two files by the link below). Namely, a function ...
6
votes
3answers
275 views
Find an envelope of the list of points
I have a list of points as you can see in the image below. From this list of points, I want to generate a filtered list of points, which is the envelope. Additionally, calculate the area under the ...
0
votes
0answers
45 views
Unable to Integrate (or NIntegrate) with Piecewise limits
Essentially, I am trying to find the following, either algebraically or numerically, where Z is defined by the piecewise function in the Mathematica code (below):
$\displaystyle{\int_0^{\infty } \...
1
vote
0answers
12 views
Convolve[…] behaves differently to that of Integrate[…] when numerically integrating the result
I am performing a convolution between two functions, and then I want to numerically integrate the result.
If I go:
...
0
votes
0answers
37 views
Numerically integrating a highly oscillatory multi-dimensional Bessel function with good precision
This is a follow up question to Numerically integrating a highly oscillatory Bessel function with good precision.
Now I am considering a three dimensional integral,
...
1
vote
2answers
94 views
Numerically integrating a highly oscillatory Bessel function with good precision
I am trying to evaluate the following integral
Integrate[Csch[w]^2 (w BesselJ[1, w Sqrt[y]/π]^2), {w, 0, Infinity}]
in an asymptotic large ...
-1
votes
4answers
91 views
Problem with NIntegrate over a highly-oscillatory integrand
I'm trying to numerically evaluate the integral $$\int_{a}^{b}\mathop{\mathrm{d}x}\int_{x}^{b}\frac{\sin(x-y)}{xy}\mathop{\mathrm{d}y}$$
using Mathematica. To do that, I the function
...
4
votes
1answer
124 views
Solve PDEs with finite difference scheme by modifying NDSolve-based solver
Motivation
As discussed here, NDSolve uses different difference orders for various spatial derivatives and the implicit design could cause trouble in certain cases....
0
votes
2answers
65 views
Finding a numerical solution and plotting it over a wide range
My problem is that I am trying to find a Numerical solution to a function of the form f(x,c)== K for x for some given values of c, K, and plot this function over a wide range of values of c.
My ...
-1
votes
1answer
52 views
Plotting and Finding Area for Discrete Points
I want to plot a graph for following coordinates and then I want to find the area from x = 900 to 1600. What is the correct path to find the area of that limit?
...
0
votes
0answers
15 views
Using RegionPlot with NIntegrate causes symbolic evaluation when integrating
I am trying to plot the regions when a certain integral is positive. Because the function has many parameters I am passing the values through two sets of rules, one containing the pair of values I ...
0
votes
0answers
31 views
Assumptions in integration
I am trying to evaluate the integral
$$ \int_0^{2\pi}\frac{D_{11}^2+2D_{12}^2+D_{22}^2+D_{33}^2}{1+e\cos x(t)}dx $$
Where $D_{ij}$ are third derivatives wrt $t$ as defined below.
...
1
vote
0answers
69 views
0
votes
2answers
49 views
Want to use NIntegrate with some unknown coefficients associated with the expressions
NIntegrate[C*x^2, {x, 0, 2}]
Here is the simple expression I want to use NIntegrate to find the value, but I am getting "The ...
3
votes
2answers
308 views
Help needed to make NIntegrate Converge
I have the following notebook (trying to caclulate the pull-in voltage of a structure):
...
1
vote
1answer
49 views
2
votes
1answer
206 views
Solve integro-differential equations
I am trying to numerically solve the following integro-differential equation and get some plots for $n(s)$ vs $s$:
$$
\dot{n}(s)-\frac{\dot{w}(s)}{2w(s)}\int_{-\infty}^s ds'\frac{\dot{w}(s')}{w(s')}(...
1
vote
0answers
35 views
Different values of the numeric integral evaluated by using different methods
Consider the space of three variables $x,y,z$ defined in the ranges
$$
\tag 1 x \in (0,\pi), \quad y \in (0,\pi), \quad z\in (0,2\pi),
$$
and the following UnitStep ...
5
votes
1answer
111 views
How to solve this equation numerically or analytically
In the paper, entitled:
A Closed Form Solution for the Pull-in Voltage of the Micro Bridge
(Link to PDF: https://pdfs.semanticscholar.org/0d31/33707b1243f6b4e3344c4fa19b831b010b8b.pdf)
... the ...
1
vote
2answers
66 views
How to force Mathematica to integrate only over the domain given by (few) step functions?
Consider the function f[x,y,z,...]*UnitStep[g1[x,y,z,...]]*UnitStep[g2[x,y,z]].
the variables x,y,z… are defined into the ranges $\{x_{1},x_{2}\},\{y_{1},y_{2}\},.....
2
votes
1answer
57 views
Quasi Monte Carlo method gives zero for the following example
Consider the example
NIntegrate[UnitStep[9-x^2-y^2],{x,0,xmax},{y,0,ymax},Method->"QuasiMonteCarlo"]
If xmax = ymax = 3, ...
1
vote
0answers
35 views
How do decrease uncertainty of Monte-Carlo integration?
I have some function of many arguments and need to integrate it over the region given by the products of Heaviside theta functions. Namely, I write, say,
...
5
votes
0answers
48 views
Details of NDSolve calling LSODA
Inspired by my question regarding the computation time of NDSolve using the LSODA backend I was wondering how NDSolve is actually calling LSODA (what arguments are sent to LSODA), i.e. what are the ...
2
votes
1answer
129 views
NIntegrate fails to converge
I am trying to compute this integral for different a with 0.0001<a<0.5,
...
2
votes
2answers
52 views
NDSolve producing message Power::infy
I am trying to solve geodesic equations in some 3D black hole spacetime. It is a coupled ODE system with boundary conditions. Due to the symmetry of the spacetime, I expect the solutions to be even ...
1
vote
2answers
142 views
Numerical integration with Dirac delta
I have some complicated function depending on many arguments $x,y,z$ and parameter $a$ multiplied by Dirac delta of another function,
$$
\tag 1 f(a,x,y,z) = g(a,x,y,z)\delta(t(a,x,y,z))
$$
I want ...
1
vote
0answers
34 views
1
vote
1answer
78 views
Simulating a combination of PDEs and ODEs
I am trying to simulate a combination of PDEs and ODEs, given below.
$$ \begin{matrix}
-L\dfrac{\partial}{\partial t}I(t,z)&=&\dfrac{\partial}{\partial z}V(t,z)+RI(t,z)\\
C\dfrac{\...
0
votes
1answer
89 views
Why does Monte Carlo integration underestimate my integral as integration range increases?
I'm having a huge problem with Monte Carlo integration. This simple example adequately shows the problem.
...
6
votes
2answers
189 views
Conductance from Landauer-Buttiker approach
I have a single-rectangular potential barrier in graphene. The transmission $T(E,\theta)$ is given by
$$T(E,\theta) = \left[1+\left(\frac{V}{\hbar v_Fk_x}\right)^2\tan^2\theta\sin^2(k_xD)\right]^{-1}$$...
0
votes
0answers
26 views
NIntegrate failed to perform the integration unless AdaptiveMonteCarlo method is chosen
I have multi-dimensional numerical integration of some function depending on one parameter. If no specification for the integration method is chosen, the output for specific values of the parameters ...
