Questions on the use of numerical functions NIntegrate and NDSolve.

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585 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
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1answer
244 views

DAE - varying initial conditions

I want to solve a DAE-system and I want to vary more than one initial conditions and to manipulate them. I looked here: Putting NDSolve into ParametricPlot But it does not work: ...
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1answer
151 views

Error messages when using NInverseFourierTransform

I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
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2answers
302 views

Problems with NDSolve and stiffness

I am trying to solve an ODE in chemical kinetics: $$\begin{align*} \frac{\mathrm d[x]}{\mathrm dt} &= -k_1 [x][y]\\ \frac{\mathrm d[y]}{\mathrm dt} &= k_1 [x][y] - k_3[y] \end{align*}$$ My ...
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1answer
242 views

double integration

I want to evaluate a double integral, but the limits of one integral is a function of the second. Like this ...
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1answer
376 views

Integrate on a logarithmic grid

I am trying to solve numerically an integral equation, and from a couple of tests I can see that the result has a strong logarithmic divergence. For my specific problem it is very important to have ...
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1answer
370 views

Applying l'Hôpital's Rule to NDSolve with Piecewise Function

OK, so I've been working on this problem for over a week and it's driving me crazy. I'm trying to solve a system of two differential equations in $x(t)$ and $y(t)$ using a "time-elimination method," ...
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1answer
84 views

Error with minimization of NProbability

I'm trying to solve the following problem: ...
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1answer
772 views

Nested NIntegrate - NIntegrate::inum: - error

I have the problem quite similar as in: Nested NIntegrate I define two functions: ...
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1answer
127 views

How to change variable that has been defined in PDE?

I have a PDE function that contains a variable (named ka). I want to plot the result of my PDE in 1 plot using several different ka values. However, I'm not sure about how to write down this equation. ...
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2answers
227 views

System of ODEs specified by large coefficient matrices

What is the best way to call NDSolve for solving a system of differential equations of the form ...
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1answer
279 views

Problem with Eventlocator Method for NDSolve

I want to solve the ode and plot the solution v[x] for different values of parameter a where ...
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2answers
296 views

NDSolve and results of the previous computations

I want to solve following system of ODEs: $ \Bigg\{ \begin{array}{} \frac{\partial C}{\partial t}=\frac{2W_b}{Rsin(\theta)}(1-\frac{C}{\gamma})+\frac{\nu}{\pi R^2}\frac{\partial C}{\partial Z} ...
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0answers
70 views

Numerical Integration/Function

I have a problem with a function defined numerically through an integral of the form: ...
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27 views

What means the definition F[t_?NumericQ] :=…? [duplicate]

I've come along a function defined in this way: F[t_?NumericQ] := NDSolve[{-u''[x] - u[x]/x == -t^2 u[x], u[x0] == x0, u'[x0] == 1}, u, {x, x0, x1}] What does ...
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50 views

Locating Periodic Orbits - Part II

In a previous post Part I I asked how could I locate the x0 position of a periodic orbit. I got only one possible solution but it does not work as I want. Let me be ...
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0answers
36 views

Order of evaluation when using Solve and Minimize

I have to solve numerically an integral, that ends up being more or less as follows: Solve[f[x]==a*Sum[Sin[x-i]*(f[i]-f[i-1]),{i,1,x}],f[x]] (not actual ...
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0answers
32 views

Real or Imaginary result of spherical bessel and hankel functions of imaginary arguments

I am trying to calculate a rather complicate expression involving Spherical Bessel and Hankel functions. My problem is that somehow for pure imaginary arguments the functions are not pure real or ...
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0answers
78 views

“General” strategy to use NIntegrate for multidimension integrals?

I don't have much experience of numerical methods for multidimensional integrals. Currently, the particular function I want to integrate is: $$f(x,y,z,p_x,p_y,p_z) = \frac{p_x^2(2 p_x x(p_y y + 4 p_z ...
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0answers
78 views

Unequal behaviour of FindRoot to two similar functions

Unfortunately, I have some difficulties to plot a function. Here is my code: ...
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0answers
34 views

How to tell NDSolve to ignore small values in choosing step size

I have a very large system of first order differential equations, which can be written (on paper) as dX/dt=F(X), where X is a vector and F is a vector function. All elements of X are strictly positive ...
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0answers
62 views

Mathematica Integrate implicit assumptions returns a function not defined in some points while NIntegrate performs integration safely

Hi guys i'm performing a standard integration with mathematica routine Integrate, the function i'm integrating is the following: ...
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0answers
63 views

Plotting a Function that contains a Numerical Integration

I'm using mathematica to plot a function that has been defined in the following way: ...
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0answers
55 views

Numerical integration with large exponents

To make a long story short, I am doing mostly analytic calculations and therefore do note have good skills in numerical integration. I have to numerical integrate the following integral ...
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0answers
83 views

How do I perform the following numerical integration

I have the following integral to evaluate numerically: $$x(t) = \frac{1}{f(t)}\int_0^{t_b} t^m (t + n)^o \sin(pt) \mathrm{d}t \quad m,n,o,p \in \mathbb{R}$$ ...
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0answers
45 views

Getting message NIntegrate::inumr: in V10; did not happen in V9 [duplicate]

I just tried making a ParametricPlot that worked error-free in Mathematica 9, but now produces errors before successfully plotting in Mathematica 10. It appears to ...
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0answers
84 views

Problem solving a Fredholm integral equation

Based on the algorithm by PlatoManiac presented here Integral equation numerical solution with NDSolve I am solving a Fredholm integral equation with the following constants and arguments: ...
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49 views

NIntegrate with and without MaxRecursion

Ran a mathematica code using NIntegrate containing an integration over spherical and normal bessel functions. 1.Would the answer in the two cases change if I use MaxRecursion with some number of ...
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44 views

Difficult to solve the equation using FindInstance and not able to solve it numerically

I hope to find the range of a which leads to non-zero solution of H when you are given a specific value of B. And I hope to get ...
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1answer
47 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 ...
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0answers
49 views

Pass model parameters to NDSolve'Reinitialize

I am wondering if there is a way to pass parameter values during the NDSolve'Reinitialize step of the NDSolve process? I've read that one way to possibly speed up repeated calls to NDSolve is to ...
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0answers
59 views

Resolving initial / boundary condition conflicts ?

This is likely very simple, but I often run into trouble with inconsistent boundary conditions for PDEs; While I know Mathematica sometimes produces "false" errors for spatial derivative conditions, ...
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0answers
99 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 ...
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40 views

NIntegrate Issue: Changing integration limits makes calculation time extremely long

After a long time developing some code in mathematica and finally getting it to work, I have unfortunately encountered an odd problem: When I change the limits of integration (and shift the function ...
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40 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: ...
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337 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 ...
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0answers
53 views

Ideas for NDSolve?

I'm currently trying to find a numerical solution to a differential equation of the form: D[W[X], {X, 4}] ==(-(1/(delta + G - (G X)/L)^2) + 1/(delta + (G X)/L)^2) ...
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0answers
94 views

Problem with using the results of ParametricNDSolve in a ParametricPlot3D

I new to Mathematica and I have a problem with certain equations. I want to plot a trajectory in spherical coordinates given by the equations: ...
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0answers
123 views

A power series expansion

Consider the function, $f(z) = z tanh(\pi z) log (z^2 + a^2)$ for some $a>0$. Now I am considering 3 different situations, $z = i(n+0.5) - i\epsilon + \delta - it$ for $n \in \mathbb{Z}$ and ...
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0answers
68 views

Solving an ODE, where the coefficients are implicit functions of time, not in closed form [duplicate]

I have an ODE, say of the first order for simplicity, and of the form, $A.x'[t] =B$. The coefficients are functions of time and x[t], not in closed form. I can define the coefficients, $A$ and $B$, ...
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100 views

an NIntegrate inside a manipulate in mathematica was working and suddenly won't work now. it says indeterminent and it doesn't make any sense why

my title says pretty much everything heres what I'm entering. NumericQ returns a false value but it was true before. Im loosing my patience because this is so ...
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0answers
166 views

Calculating the Lyapunov Exponent/Spectrum for the Duffing Oscillator

Some fellow students and I are trying to calculate and plot the Lyapunov spectrum for the Duffing oscillator (currently a test approach). Each of us has Mathematica knowledge based purely on past ...
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0answers
100 views

complicated Numerical Integration, FEM application

I am trying to calculate a 2d Integral which has another 2d integral in the integrands. here is the setup: ...
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0answers
87 views

Numerically Solving Compatible Systems of Overdetermined PDE

Is there an easy way to get Mathematica to numerically solve a compatible system of overdetermined PDE, and plot the solutions? For example, consider the "toy" example $\dfrac{\partial u}{\partial ...
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0answers
171 views

Loop integrals (quantum field theory)

I am attempting to compute the one loop contribution to the Higgs mass, and the one loop integral is somewhat difficult. I decided to try and get Mathematica to do it, to see if the answer can point ...
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50 views
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0answers
45 views

How does NIntegrate evaluate a piecewise range of x,y?

Could someone explain to me how Mathematica evaluates the following integration. ...
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0answers
165 views

Boundary Value Problem- using NDSolve or another method

I am trying to solve a set of coupled partial differential equations, with defined boundary conditions using mathematica. Here are the equations and the boundary conditions. ...
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0answers
69 views

An error message with NIntegrate and inability to plot the integrand

I took a function of x which depended on parameters on m,n,a,y and then first summed up the n from -Infinity to Infinity and then I set the other parameters to some random values and then I asked it ...
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160 views

Mapping the imaginary axis of the complex (s) plane

In this problem is very difficult to analyze the roots s. Firstly I thought that the problem is in precision, but I am not sure. The criterion which I want to obtain is that one of these roots has a ...