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8 votes

Shape of a boomerang

I do not clearly understand your question. However, if you want to plot the shape of a boomerang use the following code. ...
user444's user avatar
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7 votes

Galactic rotation speed

We can solve this problem using colocation method with Euler wavelets ang Gauss quadrature rule. First we define interval $0\le R\le Rmax$ and map interval $(0,R)$, on ...
Alex Trounev's user avatar
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6 votes

Solution of an integral equation

To solve this problem we can use iterative method described here. Unfortunately two conditions at $x=\pm \infty$ are not enough to define unique solution. Numerically we can define 2 solutions as ...
Alex Trounev's user avatar
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5 votes

Shape of a boomerang

Based on @user84456's helpful answer we can evaluate the parameters needed for the simulation (see my comment ) ...
Ulrich Neumann's user avatar
5 votes
Accepted

How do I take the integral of a real number over a complex region?

In calculus class we called the first three TeX'ed lines in the OP, the method of substitution. It's not particularly connected with complex numbers. It's just that your equation has an ...
Michael E2's user avatar
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5 votes

Solution of an integral equation

Initial solution idea Your integral equation can be reduced to an interesting system of differential equations, at least in $r=1$ case. Since $A(x)>0$ we can write $A(x)=e^{a(x)}$. Therefore $$ a(...
yarchik's user avatar
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5 votes

Galactic rotation speed

Here is a series expansion solution based on the idea that I mentioned in an earlier comment. Within the range of validity of the series expansion it leads to a result that is numerically very similar ...
Stephen Luttrell's user avatar
5 votes
Accepted

Different integral values for analytically same integrals

The integral of L[40] gives a warning that precision may be lost because of small numbers. Therefore what you can do is to use exact numbers like: ...
Daniel Huber's user avatar
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4 votes
Accepted

Trouble evaluating the following integral

$Version (* "13.3.1 for Mac OS X ARM (64-bit) (July 24, 2023)" *) Clear["Global`*"] It is more efficient to convert the ...
Bob Hanlon's user avatar
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4 votes
Accepted

How to solve this integral equation numerically?

Although the general problem in the question probably requires the methods referenced by flinty in 285076, the specific problem contained in the question's code, ...
bbgodfrey's user avatar
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4 votes
Accepted

Solution of an integral equation

A small modification of @AlexTrounev 's great answer gives a unique fixedpoint without jumps for r=0,1,2! It's only necessary to modify the iterationpart $\text{fa}...
Ulrich Neumann's user avatar
4 votes
Accepted

Algebraic solution of an equation containing an error function

$Version (* "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" *) Clear["Global`*"] You will need to use numeric techniques. ...
Bob Hanlon's user avatar
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3 votes

Is there any hope that Mathematica answers this parametric integral?

The limit of the function under integration as x->∞ is 1 therefore the integral $\int_0^{\infty } f x \, dx$ cannot converge ...
azerbajdzan's user avatar
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3 votes

Is there any hope that Mathematica answers this parametric integral?

Under those conditions the integral diverges and Mathematica shows it by ...
user64494's user avatar
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3 votes

How to give conditions and solve an integration?

Your expression generates for K=0 the squared expression $$\text{PowerExpand}\left[\sqrt{\text{FullSimplify}\left[\left(\int \frac{a^{\frac{1}{2} (3 k+1)}}{\sqrt{\frac{1}{3} a^{3 k+3} (8 \pi G \...
Roland F's user avatar
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3 votes

How do I take the integral of a real number over a complex region?

May be ClearAll["Global`*"] ode = D[f[ τ ],τ]==A; sol = DSolveValue[ode,f[τ],τ] sol = sol/.{τ->I*r,C[1]->C[1]*I} Simplify[sol]
Nasser's user avatar
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3 votes
Accepted

Galactic rotation speed

Here my third answer which solves case R==25 . This approach uses an interpolation-function (instead of wavelets or FEM) to describe the unknown function ...
Ulrich Neumann's user avatar
3 votes

Galactic rotation speed

modified: Case Rmax==25 Inspired by the interesting discussion with Alex I found a direct approach, using a simple polygonal ansatz( borrowed from FEM). It solves the original integralequation, ...
Ulrich Neumann's user avatar
3 votes

Galactic rotation speed

Here I 'll show an iterative solution. First the integralequation is differentiated D[....,R] . This finally gives ...
Ulrich Neumann's user avatar
3 votes
Accepted

Write Integral in Ostrogradsky's Method Form

...
Bob Hanlon's user avatar
  • 159k
2 votes

Write Integral in Ostrogradsky's Method Form

Defining a module to perform and display the Ostrogradski method ...
Bob Hanlon's user avatar
  • 159k
2 votes
Accepted

How to speed up this integration?

Assuming m==h and a<0<q Mathematica 12.2 states non-convergent integral: ...
Ulrich Neumann's user avatar
2 votes

Integro-differential equation with double integral

This problem can be solved with the Euler wavelets collocation method even in v.8 as follows ...
Alex Trounev's user avatar
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2 votes

How to solve the integral equation?

Replacing your NSolve[...] by ...
user64494's user avatar
  • 26.7k
2 votes
Accepted

Problem Encountered when Solving a System Consisting of Two PDEs and an ODE in a Semi-NDSolve-based Approach

This problem can be solved with using implicit Euler for time step and linear FEM for space. This method described, for example, here and here. First we transform equations to the system of ODEs and ...
Alex Trounev's user avatar
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2 votes

Asymptotic volume of intersection of n-cube with n-sphere

Using angles $\theta$ indexed by their power in the volume element with radius $r$ and equatorial angle $\phi$ ...
Roland F's user avatar
  • 3,782
1 vote

Partial integro-differential equation

modified Try Galerkin method using MeshElementInterpolation: First we set B=1 by choosing an appropriate time scale. ...
Ulrich Neumann's user avatar
1 vote

How to solve the integral equation?

For small set of equations we can solve this problem using FindRoot (without error messages) as follows ...
Alex Trounev's user avatar
  • 45.4k
1 vote

Integration by Numerical Methods

Expand your expression into a sum of simple fractions and integrate step by step over the different variables $$\text{df}=\frac{e^{-\frac{\text{Ep}^2+\text{Eq}^2+p^2+q^2}{2 \sigma ^2}} \left(\left((\...
Roland F's user avatar
  • 3,782

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