Questions on the use of numerical functions NIntegrate and NDSolve.

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0
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1answer
237 views

Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]

Starting off with the time-independent Schroedinger equation (TISE) $\quad \quad -\frac{\hbar^2}{2m} \nabla^2 \psi + V(r, \theta) \psi = E\, \psi,$ I would like to study the time evolution of an ...
0
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0answers
61 views

Integro differential eq boundary difficulties

I'm trying numericaly solve simple integro-differential equation, but have some problems with boundary conditions. System: ...
0
votes
1answer
67 views

How can I perform this integration in Mathematica? [closed]

I am new to Mathematica. I want to find the integration of the following expression: $H(f)=T\left(\frac{sin(\pi f T)}{\pi f T}\right)^2$ Here, $T=1.127e-7$ I want to integrate this function for a ...
7
votes
1answer
199 views

Detecting nearly simultaneous WhenEvents in NDSolve

I am trying to solve a system of (many) coupled nonlinear ODEs. I need to decouple some of the equations (i.e. set the time derivatives of some of the dependent variables to zero) at various points in ...
3
votes
1answer
236 views

Evaluating a numerical integration with infinity as limit

I am trying to evaluate a numerical integration (to get an expression of the constant Ω) Suppose that h[x_] := 1/(1 + a x^2) ...
-3
votes
1answer
122 views

How can I evaluate this function in Mathematica? [closed]

I am very new to Mathematica. Today I have got my license. Can someone help me to evaluate the following expression in Mathematica. I want find the values of $P$ for different $n$ $S=129$; $F_l(\...
0
votes
3answers
87 views

How do I integrate this function?

I am very new to mathematica and also new to this community. I have a problem given below, How to express this in Mathematica? $H=[2,4,10,5,12,34,42,\cdots 12]$ is a vector of size $N$. $h_n$ is the $...
0
votes
2answers
95 views

Fix my code to return a table of values

Here is a “procedural” program that we wrote in my class, implementing the rectangle rule of numerical integration: ...
1
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0answers
80 views

Passing integration constants to self defined function

I would like to evaluate an integral I am taking in cylindrical coordinates, in which the integrand contains a previously defined function. I need to pass the r and phi integrand values to this ...
0
votes
2answers
222 views

Numerical 3D Integration in Mathematica [closed]

My question in short is: Is it possible to make numerical 3D integration in mathematica efficiently? Or am I gonna have to move this to C++? I feel this problem is way too trivial to go to C++, so ...
3
votes
2answers
168 views

Integrate and NIntegrate not the same

Why am I getting two different results here? ...
0
votes
1answer
127 views

Difference between NIntegrate and Integrate results

I want to integrate a function of two variables that is defined via a piecewise function. I can compute the integral analytically as follows: ...
1
vote
1answer
665 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...
1
vote
0answers
55 views

Speeding Up the Numerical Integration of a Product of Numerical Integrands with NIntegrate

I need to solve a set of coupled integral equations within a self-consistent cycle. The final result will be functions, say $A(x)$ and $B(x)$, which are related to each other by some integrals which ...
1
vote
1answer
258 views

How to modify a PDE inside NDSolve according to an if condition

I need to solve this PDE $$\partial_tf(t,x)+\partial_xf(t,x)+k\partial_{xx}f(t,x)-xf(t,x)=0 $$ with $k\in\mathbb{R}$ and final condition $f(T,x)=1$ with $0<t<T$. My problem is how to solve ...
2
votes
2answers
342 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 post)...
1
vote
2answers
104 views

Confusion in Numerical Integration while using FindRoot

I used this code for numerical integration NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, 13}] when upperlimit of x is 13, the integral value ...
1
vote
2answers
196 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
0
votes
2answers
251 views

Multidimensional Numeric Integration

I can't manage to calculate numerically the following multidimensional integral: $I(X,Y,T)=\int_{0}^{T}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(...
0
votes
1answer
311 views

NdSolve problem :NDSolve::ndode: Input is not an ordinary differential equation

I am new to Mathematica. I am working on solving the following different equations numerically written in the code as below. Not so sure about the boundary values that depends on R (M(0)=0, n(1)=0) ...
2
votes
1answer
552 views

(NDSolve) Non-linear 2nd order ODE, regular singular point (looking for good methods for this problem)

I am solving this set of non-linear 2nd order ODE by NDSolve, $$r^2\frac{d^2f}{dr^2} = 2f(1-f)(1-2f)+\frac{r^2}{4}h^2(f-1)$$ $$\frac{d}{dr}\left[r^2\frac{dh}{dr} \right]=2h(1-f)^2+\lambda r^2(h^2-1)h$$...
2
votes
0answers
70 views

Enforcing WorkingPrecision in NIntegrate

I have a very complicated 2D integral that I need to calculate repeatedly, and I'm trying to speed it up a bit, since at the moment it's taking a couple of days to complete. One thing I've noticed is ...
1
vote
2answers
117 views

Simple integration with assumption

I would like to evaluate the following simple expression NIntegrate[Re[Exp[I*Omega*t]], {t, 0, 2 Pi}] for Omega real, but ...
2
votes
2answers
360 views

NIntegrate over a list of functions

This question is the result of these other two questions. Question 1 and 2. I thought it would be better to ask a new question rather than deleting previous one. I think When ...
0
votes
1answer
233 views

Numerical integration and plotting

New to Mathematica, and trying to numerically evaluate two integrals: ...
5
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1answer
213 views

Slow exponential evaluation over lists

This question,which is still unanswered, might be relevant because it involves NIntegrate over lists and it also has Exp. In ...
0
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0answers
56 views

A problem about NIntegrate the smaller eigenvalue for a matrix

Define a matrix and a function as ...
1
vote
1answer
136 views

Quantum Physics question [closed]

I'm not sure if anyone here would be able to help me. But if you know a more appropriate place where I could ask for help, please let me know. So here's the question: And here's my attempt at ...
1
vote
2answers
263 views

Initial Step Size for NIntegrate

I am using Mathematica to numerically integrate a numerically-defined function (from an interpolation and data). This function has a sequence of somewhat unevenly spaced sharp peaks which dominate ...
1
vote
1answer
282 views

Slow evaluation of NIntegrate when used as a pure function

I asked a perhaps related question here. Here is my code in below. The goal is that to define a function which must be integrated numerically. The function itself first is calculated over different ...
3
votes
1answer
620 views

Numerical integration's speed

Consider this numerical integration of Bessel function: Do[NIntegrate[BesselJ[2, x], {x, 0, 10000}], {i, 1, 100}] // AbsoluteTiming {4.033403, Null} This is ...
7
votes
2answers
363 views

How to force Mathematica to throw an error for NIntegrate

Consider this: NIntegrate[BesselJ[2, x], {x, 0, Infinity}] 0.9999999999904574 This is the correct answer. Now: ...
6
votes
1answer
307 views

Strange Behaviour of NIntegrate

I found some of the values remained unevaluated using the following code Table[NIntegrate[Sin[i x]/((2^x + 1) (Sin[x])), {x, -Pi/2, Pi/2}], {i,70, 90}] Pick them ...
2
votes
2answers
582 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
151 views

WhenEvent error in NDSolve

I’m trying to solve a discontinuous differential equation where there are lost of energy when the trajectory cross the discontinuous manifold. The code I used was ...
1
vote
0answers
106 views

Extrapolation of area for a 2D integration

I have a set of points distributed almost uniformly in a certain area of a 2D plane as follow: An example of data points (orange) data = {{0.919443, 1.68921*10^-22}, {0.262277, 1.46747*10^-22},...
5
votes
2answers
182 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
1
vote
2answers
378 views

Real integral evaluates to imaginary number

The following integral:Integrate[Exp[-2/3 Log[1 + x^3]], {x, 0, 1}] is evaluating to an imaginary number. Its closed-form expression should be ...
2
votes
1answer
209 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
0
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0answers
74 views

NDSolve dependence on initial values

I'm checking some results in this paper and I'm currently having some issues with a numerical integration of a set of differential equations using NDSolve (section 2 and 3.1-3.2 in the paper). I'll ...
0
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0answers
122 views

Divergence in the initial value problem solved by Ndsolve

here is to ODE I need to solve: ...
0
votes
1answer
106 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
1
vote
3answers
117 views

I know the lower limit of an integration as well as the integral. How to find the upper limit of the integration?

I used the following code. NV[x1_, x2_] := NIntegrate[3 x^2, {x, x1, x2}] FindRoot[NV[0, t] == 3, {t, .001}, PrecisionGoal -> 20] Output: NIntegrate::...
2
votes
2answers
277 views
2
votes
2answers
418 views

NIntegrate 2D highly oscillatory function

I am trying to integrate a function, and the error I get is greater than the result. So I need to calculate ...
1
vote
1answer
155 views

Problem with NIntegrate over a user-defined region

I define a region as follows: ...
5
votes
1answer
408 views

Obtaining an NIntegrate error estimate

Is there a way to extract the error that Mathematica estimates when calculating a numerical integral using NIntegrate? Internally Mathematica must keep track of ...
0
votes
1answer
107 views

NIntegrate vs. summation

I' m interesting in distributions of points on sphere, plane figures etc. Especially for small number of points: 1, 3, 7, ... It seems that good criterion for uniformity of distribution is some ...