Questions on the use of numerical functions NIntegrate and NDSolve.

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2
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1answer
45 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. ...
2
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1answer
403 views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
2
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1answer
601 views

Infinite Expression Error from NDSolve

I am trying to solve a differential equation numerically. So I have ...
2
votes
2answers
617 views

How to remove a singularity with WhenEvent

Bellow I have a differential equation which hits a singularity at low values of t. What I want to do is somehow utilize the WhenEvent command in order to replace ...
2
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1answer
82 views

Numerical integration with OwnValues

Say I have a symbol with an OwnValue a = y And we define an integration like this ...
2
votes
2answers
689 views

Making NIntegrate behave like a listable function

I have a function defined by $$f(t)=\int\limits_0^t g(x) dx$$ $g(x)$ is a complicated function (specifically the Mittag-Leffler function which has recently been implemented in Mathematica 9 as ...
2
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1answer
251 views

How to solve a system of ordinary differential equations contain a interpolating function?

I'm wondering how I can solve a system of ODE that has a interpolating function? For example, z and y are ...
2
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1answer
845 views

Solving a PDE containing DiracDelta

I want to get the answer from a PDE: $$\begin{align*} \frac{\partial \rho(r,t)}{\partial t}&=Dr^{-2}\frac{\partial}{\partial r}r^2h(r)e^{-U(r)}\frac{\partial}{\partial ...
2
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1answer
590 views

How to use NDSolve to track a deviation from equilibrium?

i have a task to find a event, to achieve this i think need to integrate until a constant function suddenly breaks the equilibrium and give a sharp peak. I think that EventLocator should work, thus ...
2
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1answer
79 views

Error accumulation in NDSolve?

I'm trying to solve this system of ODEs numerically: $$\vec{Q} = \vec{P} \times \vec{Q}$$ where vectors $\vec{P}, \vec{Q}$ have 3 components: $$\vec{Q} = \left( Q_1, Q_2, Q_3 \right) $$ $$\vec{P} = ...
2
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1answer
120 views

Solving an integral equation numerically

my problem is: I get the result of definite integral and now I need to find the upper limit for the same integral but with opposite sign value so f2=-f1. ...
2
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2answers
132 views

Approximation of definite integral by parabolas

This question is related to Trapezoid approximation to definite integral. As promised, I am now asking about how to draw approximation of integrals by parabolas. I tried to modify MarcoB's code, and I ...
2
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1answer
60 views

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function?

How to NDSolve a set of equations, one of which itself contains NIntegrate of a desired function waited to be solved by NDSolve first? For example, ...
2
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1answer
177 views

Catastrophic loss of precision

while I am trying to solve the double integral in the range of 0 to Infinity (for both the integral) it give me the error Catastrophic loss of precision in the global error estimate due to ...
2
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1answer
107 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
2
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1answer
95 views

How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
2
votes
1answer
229 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} ...
2
votes
1answer
888 views

Obtain a stable solution using NDSolve

I am trying to solve a partial differential equation using NDSolve. When I am not specifying any method options with NDSolve, it ...
2
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2answers
391 views

Strange Behavior of NDSolve

I am trying to evaluate the following ODE numerically: ...
2
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2answers
791 views

Putting NDSolve into ParametricPlot

I am having issues using Manipulate to plot the (numeric) solution to an ODE for different parameter values. I have a code that has several stages, which seem to ...
2
votes
1answer
140 views

Differences between ParametricPlot3D and NIntegrate

I have a function $f : \mathbb{R} \rightarrow \mathbb{R}^3$ defined in a rather nasty way in mathematica however it's a smooth function and what not. I am interested in $f'[t]$ and when I run it ...
2
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1answer
399 views

How can I handle curve singularity in this NIntegrate integration?

Yesterday I asked a question about the non converging integral. Woods told me that it is due to the function which has a singularity along a line which passes through the integration region. (Why ...
2
votes
1answer
630 views

Problem with NIntegrate in NonlinearModelFit

We are receiving many error messages when using NIntegrate with NonlinearModelFit. Here is a much-simplified version of the code. It arrives at the correct answer after several messages saying that it ...
2
votes
2answers
852 views

Problem with NDsolve for a system of equations

I want to solve a system of differential equations which is not very complicated, but I cannot handle the problem with mathematica!! Please have a look at the problem and result and help me with your ...
2
votes
1answer
42 views

Integrate and NIntegrate combined, giving MaxPrecision error

I am trying to integrate the following : ...
2
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1answer
74 views

Forcing Exact Outputs for Integrate [closed]

I'm trying to compute the following triple integral: ...
2
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2answers
235 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 ...
2
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1answer
110 views

NIntegrate and Integrate giving different results for ill-behaved function

I'm trying to integrate the following function with Mathematica 8: $$ I(a,b)= \int_0^1 \mathrm{d}x\int_0^1\mathrm{d}y \,\theta(1-x-y) \frac{1}{x a^2-y(1-y)b^2},$$ where $\theta$ is the Heaviside ...
2
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1answer
156 views

2D Fourier transform of a few (4) disjoint discs on a plane

I'd really appreciate some advice. Short Version I'm trying to calculate the following $$ ...
2
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2answers
435 views

How can i integrate over a set of data

i need to integrate over my data, which is denoted as {q, I},here I is the Intensity i need to obtain the form of the following integration( its not a numeric integration, because it contain x, next ...
2
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1answer
191 views

Internal Shooting Method of NDSolve in combination with NDSolve`Reinitialize?

To explain my problem, I am trying to extend the BVP problem example from the help that illustrates how to use the shooting method of NDSolve: ...
2
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1answer
406 views

Numerical Integration with Variable Parameters

So I want to numerically compute the integral of a long complicated expression over a specified domain (in this case an ellipse). I know how to use a Boole function to sample within the ellipse, but I ...
2
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1answer
122 views

Differentiating a function that has NIntegrate within it

I am something of a novice with Mathematica. I have written the following code; ...
2
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2answers
123 views

Definite Integral. Perfomance problem

I have a notebook in Mathematica 4. I'm trying to convert it to use in Mathematica 9. One of the problem is the long computation of definite integral. In Mathematica 4 the result of the following code ...
2
votes
1answer
163 views

Evaluation of the second argument to NIntegrate

The expression Integrate[x^2, Flatten[{{x},{1,2}}]] evaluates properly, to $\frac{7}{3}$. However, ...
2
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1answer
564 views

Differential equations: Solving a singular/nonlinear ODE using NDSolve

I am trying to numerically solve a rather horrible looking singular/nonlinear ode: A*(y''[x]/y[x])'' +y[x]^2==1 on the interval ...
2
votes
1answer
419 views

Limitations of ParametricNDSolve family w.r.t objective functions

Observation: I can see even for very simple modification in case of an scalar objective involving an definite integral in time ParametricNDSolve fails. Here is an ...
2
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1answer
321 views

Which integration strategy to use for this product of polynomials?

What would be the ideal integration strategy for a function like this: $$f(x_1,x_2,\dots,x_N)=\prod_{i=1}^Nx_i^{c_i}\Theta(x_i-p_i)$$ where $x_i,p_i\in \mathbb{R}$, $\Theta$ is the Heaviside function ...
2
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1answer
168 views
2
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1answer
70 views

gaussian integration

I'm new on Mathematica and I am an engeneer with only a little base of numerical computation. I have to integrate a trigonometrical function numerically with a Gauss integration. The function is: ...
2
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1answer
58 views

Why isn't Table iterator value inserted in failed NIntegrate arguments?

Consider this simplest example: Table[{z, NIntegrate[f[x], {x, 0, z}]}, {z, {1}}] Here f is not defined, so ...
2
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1answer
121 views

How to use slots and patterns to reduce repetitive calculation?

This is kind of complicated... How can we make MMa calculate values of a function before doing multiple pattern or slot substitutions? Answers to similar questions didn't cover the case where the ...
2
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1answer
94 views

StateResponse is non-deterministic

I observed non-deterministic behaviour in StateResponse. Let's look at an example. ...
2
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1answer
102 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 ...
2
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1answer
336 views

How to use NIntegrate in a purely numerical mode?

I have a function that is defined as the smallest root of a given polynomial. Something like this: ...
2
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1answer
183 views

Plotting Laplace's equation on an infinite domain

I am trying to plot my solution to a Laplace equation on an infinite domain. However, when I try to plot it, Mathematica just runs with nothing happening. ...
2
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1answer
427 views

Avoiding zero (empty set) solution with NDSolve

I'm trying to use NDSolve for a chemical kinetics equation where the rate of conversion is given by this relationship as typed in Mathematica: ...
2
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1answer
342 views

Numerical integration involving Inverse Normal CDF

I'd like to evaluate the following numerical integration using Mathematica $$ \ \int_0^T\int_0^\infty xe^{-0.04 s}g(x,s) dxds\ $$ where g(x,s) is a Gaussian copula function with say, marginal ...
2
votes
1answer
351 views

How to integrate ParametricNDSolve solution with respect to a parameter?

I have just upgraded to the new version of Mathematica because of its new built-in ParametricNDSolve function. I need to solve a first-order non-linear ordinary ...
2
votes
1answer
316 views

Using NDSolve solution as initial condition for another NDSolve

I have solved a PDE numerically using NDSolve, and I now need to be able to use that solution as an initial condition for another ...