Questions on the use of numerical functions NIntegrate and NDSolve.

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Imaginary number appears in Integrate [closed]

I had a problem in the following code because when I use Integrate, there will always be imaginary number in the result. I put my code here. The satisfactory result should look like eq 9.138, which I ...
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0answers
47 views

How to find out how Mathematica performed an integration? [duplicate]

In terms of integration, I usually utilize Mathematica 9 to compute scattering amplitudes in quantum field theory. Recently, I employed it to compute a particularly difficult integral, and it ...
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93 views

Monte Carlo integration with random numbers generated from a Gaussian distribution

I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know. How can I change ...
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1answer
105 views

How to calculate the following integral of the multiplication of two Bessel functions?

This integration has an analytical solution and its behavior is described by 1/r^2 function, but Mathematica gives some weird oscillating answer. Can anybody explain this and help me overcome this ...
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60 views

Mathematica exit when calling plot. Bug?

I'm currently studing the behaviour of some integral for which I cant find an analytic solution. As this function depend on a vector on the unit sphere, I first defined it with 3 parameters before ...
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31 views

Integration of any interpolation generates invalid comparison errors [duplicate]

Integrating a simple interpolated function as follows generates invalid comparison errors. ...
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87 views

Choosing PrecissionGoal and AccuracyGoal for decomposed integral with NIntegrate

Assume I have a complicated integral $I$ which can feature all kinds of difficulties like infinite interval, rapidly oscillatory integrand, integrable singularities and numerically almost singular ...
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47 views

ParametricNDSolve and ProcessEquations

I have a question regarding NDSolve`ProcessEquations and ParametricNDSolve. When using the regular NDSolve we have the option to divide the integration into the three steps ProcessEquations, Iterate ...
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223 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
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1answer
69 views

Two dimensional NIntegration failure - non-numerical values

I've got this function: E0[x0_, y0_, z_]:= A/w[z]*Exp[-(x0^2 + y0^2)/(w[z]*w[z])]*Exp[(I*2*Pi*(x0^2 + y0^2))/(λ*2*R[z])]*Exp[I*ϕ[z]]; Where the ...
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0answers
87 views

NIntegrate doesn't work

I have a function, Dx[s] (defined in a module) which I can plot: Plot[Dx[s], {s, 0, GetLatticeLength[]}] However if I try ...
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160 views

Jumps in NDSolve results

I need to compute using NDSolve routine, some function $F(x)$, having two possible values $F_1(x)$ and $F_2(x)$ depending on whether the argument exceeds some ...
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90 views

why maxrecursion didn't work if I specify singularity in NIntegrate

I study sigularity specification and MaxRecursion in NIntegrate. And find something unusual. first I define a function δ[x_, y_: 1/100] := 1/π*y/(x^2 + y^2) ...
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74 views

Integrate boundaries defined as equations

Have you guys ever needed to define Integrate boundaries as equations? I tried to submit the equation as was written in original text but it seems that mathematica can't understand it. ...
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356 views

triple NIntegrate fails

Here's m problem simpler in terms of codes ...
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221 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
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274 views

Cauchy principal value integral of a list of numbers. How?

I have a list of numbers that are numerical samples of a function for which I need to find the Cauchy principal value integral. I thought I should be able to combine Interpolation with Integrate to do ...
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657 views

NDSolve: methods and step size choosing

I am looking into the documentation of NDSolve[]; more precisely how this function chooses the StepSize and how it chooses which ...
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309 views

Solving homogeneous Fredholm Equation of the second kind

I am trying to solve a homogeneous Fredholm integral equation of the second kind, i.e. $\lambda y(x) = \int\limits_a^b e^{i[\phi(t)+k(t-x/M)^2]} y(t)\,dt$ where $\lambda$ is the eigenvalue (to be ...
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1answer
369 views

NDSolve diffusion equation over/underdetermined

I have a feeling the solution to my problem is very simple… but my knowledge of differential equations is pretty weak. I am trying to solve a scalar diffusion equation (used in NMR spectroscopy, but ...
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247 views

Adapting NDSolve to circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a ...
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406 views

How can I speed up numerical integration of multidimensional integral?

I am numerically solving an integral equation that contains a double integral. I have managed to get a solution but it takes forever. I am wondering if there is a way to speed up numerical integration ...
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573 views

Speed up Numerical Integration

EDIT: I need to evaluate a very complicated multi-dimensional Integral. The dimension of the Integral depends on a variable j. Let's make my point clear with the ...
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273 views

NDSolve Convergence test failure and significant effect of DifferenceOrder on eventual results

I am solving a non linear partial differential equation with what I call free boundary conditions (solid mechanicists would know this as simply supported). I realized that this boundary condition ...
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202 views

Integrating over a region without singularity gives an error indicating the function has singularity in that region

I have the following 2D region over which I want to integrate a function: ...
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1answer
449 views

NDSolve does not give me the expected solution

I have an assignment where I need to compute chemical reactions by solving ODEs. I use NDSolve to do this. However, for one problem it does not give me the ...
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1answer
54 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 ...
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2answers
128 views

Problems with NIntegrate

I'm having trouble to do the following numerical integrations: ...
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2answers
614 views

Plotting multivariable integration

If I have a multivariable integration like NIntegrate[x^2 + y^2, {x, 1, 5}, {y, 6, 10}] But I need to plot its result in terms of ...
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1answer
318 views

NIntegrate Error-Estimate Question

When I do some complicated 4-dimensional integral numerically, Mathematica tells me its estimate for the value of the integral, and its estimate for the value of the error in the calculation. The ...
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1answer
120 views

Differential Equation help

I have a differential equation that looks like this: ...
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3answers
104 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 ...
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1answer
130 views

Zooming into Parametric Animation Plot that Uses InterpolatingFunctions

I have an interplanetary trajectory solver that calculates a spacecraft route from Earth to Mars, and I am trying to zoom into the spacecraft when it reaches its Mars intercept orbit but am having ...
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1answer
68 views

NDSolve accuracy related problem

I want to solve this equation: ...
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2answers
126 views

How to numerically integrate this integral?

I want to integrate the function funcin (spherical coordinates). ...
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1answer
268 views

What is the correct way to use NIntegrate inside the FindMinimum function?

I'm having minor issues with the FindMinimum function when using NIntegrate inside. The functions work perfectly well but I get ...
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1answer
2k views

Stategies to avoid NIntegrate::slwcon error

I am trying to numerically evaluate an integral whose integrand depends on two parameters, say $(a,b)$ and when $b\gg 1$ I suspect (although it's not guaranteed) that the integrand is very small. Thus ...
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1answer
110 views

NIntegrate failling on floating value

I'm trying to take the following integral NIntegrate[ ((Sin[Q 1]-Q 1*Cos[Q 1])/(Q 1)^3)^2 * S[Q,0.4,2] * Q BesselJ[0,0.5Q] , {Q,0,Infinity}] ...
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2answers
739 views

nested numerical integration: not valid limits?

I encountered an error when I was hoping for some Mathematica (8.0.4) magic sparing me to code up numerical integration, function approximation and root-finding myself. The broader context and the ...
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1answer
86 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 ...
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1answer
37 views

Error message from NDSolve using WhenEvent

I am working with the following NDSolve expression: ...
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1answer
105 views

Better way to check conservation in NDSolve

The partial differential equation in the NDSolve below is conservative (by construction) of $\int_{-1}^{+1} p(t,z)\ dz$ for all $t$. ...
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1answer
132 views

I integrate a real function, I want a real result [closed]

I want to count some integral in Mathematica (actually, check that this integral is zero...) I arrive to an answer which has a zero real part but has some imaginary part! Why? This could be a mistake ...
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1answer
97 views

Question with ParametricNDSolveValue

When solving the following system: ...
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2answers
180 views

Is there a better way to approximate some graphs of integrals than interpolation?

I'm still pretty new to Mathematica so my apologies if this is a dumb question. I wanted to plot some integrals of functions for no particularly good reason, but the only decent way I could come up ...
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1answer
127 views

Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
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2answers
343 views

NDSolve solution for driven damped pendulum diverges

I want to solve numerically for the system of the driven damped pendulum using Mathematica. This is the second-order nonlinear equation \begin{equation} \ddot{x} + 2 \beta \dot{x}+ \omega_0^2 \sin ...
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1answer
52 views

Compute integral symbolically

I want to compute the following integral: ...
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1answer
126 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 ...
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1answer
52 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 : ...