Questions on the use of numerical functions NIntegrate and NDSolve.

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4
votes
1answer
204 views

Efficient Dyson series implementation

I'm trying to implement a Dyson series \begin{array}{lcl} U(x,x_0) & = & 1 + \int_{x_0}^{x}{dy_1V(y_1)}+\int_{x_0}^x{dy_1\int_{x_0}^{y_1}{dy_2V(y_1)V(y_2)}}+\cdots \\ & &{} + ...
4
votes
2answers
148 views

NDSolve not returning the expected solution

I'm trying to simulate a simple circuit with Mathematica. The equation of the circuit is $R \dfrac{dQ}{dt} + \dfrac{Q(t)}{C} = f_{sig}(t)$. This is the definition of $f_{sign}$, and the function ...
1
vote
1answer
179 views

Numerically integrating solution obtained from NDSolve method

In the following example, $u(x)$ is found numerically using NDSolve method. ...
-2
votes
2answers
337 views

Use MATHEMATICA to calculate the volume of the solid [duplicate]

Use MATHEMATICA to calculate the volume of the solid that results when the region enclosed by the given curves is revolved about the x- axis. f(x)=Pi^2 Sin[x] Cos[x]^3, f(x)= 4 x^2 x=0, x=Pi/4
4
votes
2answers
327 views

Approximate value for the area between the curve

I've got this task: Use Mathematica to obtain an approximate value for the area between the curve $y=1/4$ and the x-axis over the interval $[1,2]$ with $50$ subintervals using the left ...
1
vote
2answers
686 views

Computing 10-dimensional volume of a 9-sphere [closed]

I'm trying to compute 10-dimensional volume of a 9-sphere with radius r using Monte Carlo. ...
2
votes
3answers
382 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
1answer
98 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
5
votes
2answers
152 views

Example of Integrate applying a numerical evaluation N

Here is a minimal example: Integrate[(a[1] + x)^2, {x, 1., 2.}] 2.33333 + 3. a[1.] + 1. a[1.]^2 The problem is that ...
8
votes
1answer
206 views

How do I speed up a plotting of NIntegrate when repeated multiple times inside Plot?

I am studying a set of functions (many of which I know only as a definite integral) and I have assembled into a list. Here is a sample: ...
2
votes
1answer
49 views

Imaginary term in Integration procedure

How do you remove the imaginary term in the integrated output? Compare the outcome from the operations below. The first operation yields an imaginary term, while the second one has none. ...
6
votes
3answers
420 views

Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
3
votes
1answer
1k views

Test a wooden board's vibration mode

Here is a wooden board, with dimensions shown on the picture below. How we can use Mathematica's newly build-in finite element analysis features to show the different modes of its vibrations. Assuming ...
8
votes
2answers
217 views

Why is mathematica giving wrong and incomparable results for the integral?

1) Integration of Gaussian Distribution with $(x,y,z)$ ranging from $-\infty$ to $\infty$ gives 1 as expected using this command in mathematica. (Total Probability = 1) $\sigma = 200000$ and ...
2
votes
1answer
237 views

How can I reduce computation time while still obtaining a good approximation for my function?

I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes. I have this function: $J_p=\sum_{m,n=1}^{\infty} ...
8
votes
2answers
383 views

Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
17
votes
5answers
483 views

Mismatch between numerical and analytic evaluation of an integral

I evaluated the following integral $$\int_0^1 \sqrt{r} \left | \cos \left(\left(k+\frac{1}{2}\right) \pi r\right)\right | dr$$ ...
1
vote
2answers
148 views

How to integrate a function which is only known at discrete points

I have an integration to do. I want to integrate. $\int_0^\infty sin^2(2\pi t)f(t)dt$ where $f(t)$ takes values from an array in the form $\{t,f(t)\}$ The time steps in the array is 1.1s. Can you ...
3
votes
2answers
634 views

What is the proper way to operate on interpolating functions?

I am trying to multiply an interpolating function by -1. If I do this Mathematica does not seem to allow any further operations. Bear with me while I generate the Interpolating Function in question. ...
1
vote
2answers
161 views

Integral with unreliable result

I want to calculate $\int_R^1 \sqrt{r} |\cos((k+\frac{1}{2})\pi r)|dr $ and I get a result from Mathematica. Then I try to check the result putting the value of $k$ and $R$, (k=1 and R=0.5) in the ...
0
votes
1answer
85 views

Using ImplicitRegion to define an ellipse around Multinormal distribution for integration

I have both a 2D 'MultinormalDistribution', and also a single xy point, and I would like to be able to calculate the probability of this point (given the multinormal distribution) and also plot an ...
1
vote
2answers
105 views

Evaluation of a large integral

I have a complicated large integral I want to evaluate (does not have a closed form, need an approximation), but Mathematica seems to keep "Running...". Is there any way to make Mathematica use more ...
1
vote
0answers
204 views

NDSolve PDE, not enough boundary condition?

The PDE that I want to solve is: $$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ...
1
vote
1answer
139 views

Numerically Integrating to find a Maximum using NDSolve

I am trying to numerically find an equilibrium (maximum) of a function using its differential. The following is a simplified version. ...
2
votes
1answer
117 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
1
vote
0answers
197 views

Numerically solving a 2D oscillating integral [closed]

I'm having trouble solving this integral numerically: ...
3
votes
1answer
124 views

NDSolve break condition

I'm solving a differential equation numerically by NDSolve[{p'[r] == -function[r,p[r]], p[0] == pcenter}, p,{r, 0, rmax}] with function>0. At some r, p[r] ...
3
votes
4answers
220 views

NIntegrate Trapezoid rule with even subdivision producing poor results

NIntegrate[x^2, {x, 5, 9}, Method -> {"TrapezoidalRule", "Points" -> 2, "RombergQuadrature" -> False}, MaxRecursion -> 1] returns the ...
0
votes
1answer
75 views

Compute integral symbolically

I want to compute the following integral: ...
0
votes
1answer
196 views

Numerical solution of the hyperbolic equation

I am trying to solve the following hyperbolic equation with given boundary conditions: I choose as initial condition $u=1$, and evolve the above hyperbolic equation until reaching a stationary ...
0
votes
2answers
648 views

Problems with NIntegrate

I'm having trouble to do the following numerical integrations: ...
0
votes
3answers
336 views

How to display the value of a very small number instead of “0.” [duplicate]

I need to perform an integration. There is one particular value, which may be very small that is showing up as 0.. Is there any command in Mathematica 9 that will ...
1
vote
1answer
139 views

Integrate and NIntegrate yield different results for double integral

Evaluating a double integral with bivariate normal distribution yileds widely different results depending on the method used. I define a bivariate normal distribution with ${10, 3}$ and ${8, 1.5}$ as ...
0
votes
0answers
115 views

To solve an equation

I am trying to solve the equation: Solve[Re[Integrate[(2 c - (r^2) Exp[- I 1.4746])^(0.5), {r, 0, 31.7576}]] == 2.1216, c] I want to integrate an expression in ...
3
votes
0answers
108 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 ...
1
vote
2answers
122 views

Problem evaluating a complicated integral

Apologies for stating my problem poorly in the first instance, thank you for the help in narrowing down the issue. Problem For those interested, it's for the exact unbiased inverse of the ...
4
votes
0answers
146 views

How to specify the time variable for NDSolve

I recall that it is possible to specify which independent variable is the "time" variable in NDSolve, but I can't find it documented anywhere. Does anyone recall ...
1
vote
0answers
123 views

Speeding up the numerical integration of a certain function

I'm using the following function f[t_] := 3/4 t^-3 NIntegrate[(x^4*Csch[x/2]^2), {x, 0, t}, Method -> {Automatic, "SymbolicProcessing" -> 0}]; I ...
0
votes
1answer
133 views

How to get correct numerical integration which should be zero? [duplicate]

I want to numerically integrate function berrycur over kx and ky. The definition of berrycur is given at the end of the ...
0
votes
1answer
1k views

wolfram mathematica intersection of two surfaces [duplicate]

I use wolfram mathematica. There is a function of two variables which defines the surface z = f(x,y), the second surface is defined as z = const. How to find the line of intersection of these two ...
-1
votes
2answers
100 views

Strange numerical integration result

I write a function called berrycur[kx,ky] which I will give at the end of the question, and want to numerically integrate this function over {kx, -2π, 2π]}, {ky, 0, ...
0
votes
0answers
46 views

Comparing NIntegrate with definite integration

I want to calculate without error a sum of double integrals with the following definitions for the functions within them: ...
0
votes
1answer
84 views

Numerical integration with purely numerical integrand

I'm trying to perform a numerical integral with an integrand that should not be manipulated with any symbolic preprocessing whatsoever. Consider the following simple test : ...
1
vote
0answers
1k views

NIntegrate: integrand has evaluated to non numerical values

I have pasted a code that has been giving me some trouble and errors when I try to compute. ERROR: "The integrand 1435.1232 E^(-6.4703566*10^6 s^2) deEntrance[s,phi]^2 has evaluated to ...
1
vote
0answers
276 views

NIntegrate (multi-dimensional integral)

I am interested in the numerical evaluation of the following integral: $\int \prod_{i=1}^n dx_i \delta(\sum_{i=1}^n x_i) \prod_{i=1}^n f_i(x_i)$ where $f(x)$ is a complicated function. Unfortunately ...
3
votes
2answers
294 views

Integration and Fourier transform

I would like to calculate the distribution function from the characteristic function. There is a formula given as $$F_X(x)=\frac{1}{2}+\frac{1}{2\pi}\int_{0}^\infty \frac{e^{i w x}\phi(-w)-e^{-i w ...
5
votes
2answers
1k views

Calculating the area under a curve, but above a certain threshold value

so here I am with a time series of data (hours (t) and corresponding measurements (a)). ...
0
votes
1answer
181 views

NIntegrate: Catastrophic loss of precision

Below is a simplified code that I am trying to evaluate. I am basically getting the rms value of a Wakefield function. When I finally try to evaluate the rms, I get an error. Any help would be greatly ...
3
votes
2answers
160 views

NIntegrate returns zero for non zero integrand, 4d Integration

I am trying to calculate the following integral. ...