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7 votes

Symbolic integration and numerical integration yield very different results

The problem is not Integrate, but the numerical evaluation following Integrate. Consider for example ...
  • 7,468
6 votes
Accepted

Why does smooth initial condition involving Piecewise cause mxsst warning?

Aha, after playing with NDSolve for 10 years, I find the answer of my first question in this site! Short Answer I don't think my initial condition has that kind of ...
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5 votes

Evaluating an integral symbolically seems impossible

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6 votes

Evaluating an integral symbolically seems impossible

Do you have an idea You can not do numerical integration because you had z inside the integral which had no numerical value. Adding ...
  • 116k
4 votes

Solving a system of ODEs with the Runge-Kutta method

First of all, I'd like to emphasize that, if you just want to solve an initial value problem (IVP) of ordinary differential equation (ODE) or ODE system, please use ...
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1 vote

How to solve the error "Delay partial differential equations are not currently supported by NDSolve"?

This system can be solved with using method of lines. For this we introduce discrete variable grid instead of $\tau$ and differentiation matrix ...
  • 35.3k
4 votes

Can this type of function be plotted faster using NDSolve instead of NIntegrate?

Note: This is an extended comment. This integral can be expressed in terms of the MeijerG special function: ...
  • 7,468
6 votes

Can this type of function be plotted faster using NDSolve instead of NIntegrate?

How can I apply NDSolve to this function? Do you want to apply NDSolve or do you want to plot the integral faster? The plot can ...
3 votes
Accepted

Trouble finding inverse of a function

Look at your data: ListLinePlot[UsvsL, AxesLabel -> {"U", "L"}] Note that for some Ls there two Us. Therefore the inverse function is not ...
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8 votes
Accepted

Issues with FindRoot. Getting error: FindRoot::eqlist: In the first argument {True,z1==0} only some of the components are equations

As pointed by Nasser, it's a matter of evaluation order. Simplest solution is to add Evaluated -> False: ...
  • 55.3k
5 votes
Accepted

How to speed up numerical integration?

We can speed up with using precision and accuracy options. First, we compute without options for comparison. ...
  • 35.3k
2 votes

Problem with NDSolve for 1st order non-linear system of PDEs

There is exact solution to this problem. First, let put $x=x(u), y=y(v)$, then we can use DSolve as follows ...
  • 35.3k
3 votes

Plot eigenvalues of fractional Laplacian in 1D

We can compute eigenvalues with using Haar wavelets collocation method as follows (see also our code here) ...
  • 35.3k
1 vote

How to plot the result of NIntegrate when integrand has parameters?

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  • 126k
1 vote

How to plot the result of NIntegrate when integrand has parameters?

We can use NumericQ and ReIm to plot this function. Also, it is better to divide f into two ...
  • 35.3k
1 vote

Using NDSolve for Integro-Differential Equations

This question has no answer 9 y and 4 months. While this system could be solved even in v.1 with using FindRoot only. First, we solve equations at $\alpha=0$, then ...
  • 35.3k
1 vote

How to solve ODE Bernoulli type equation plus a constant?

Actually the ode $\frac{dx}{dt}=a x- b x^c$ is not Bernoulli. It is simply separable since $a,b$ are constants. The same with $\frac{dx}{dt}=a x- b x^c+d$ is separable. Bernoulli has the form $\frac{...
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0 votes
Accepted

DiscretePlot of a function containing Nintegrate under Sum

NIntegrate has problems, because integrand is highly osccilatroy. But this can all be done with Integrate in 8 seconds. ...
  • 16.9k
1 vote

Numerical integration of numerical function

One "book" method (that is, as recommended in the documentation) is to use Indexed instead Part and the ...
  • 222k
1 vote

Numerical integration of numerical function

If I understand you right, you could always start easy. No need to make everything very short. Later, once it is working, you can always improve and shorten the code if needed. So you could do ...
  • 116k
0 votes

Series expansion of the integral from its numerical values

Since the problem reduced to finding accurate coefficients in Taylor series, I think the best method is to use difference derivatives. It worked well in my case and the ND function produced some ...
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0 votes

Series expansion of the integral from its numerical values

As the exponents of y are not important, we can as well set them to "1" to make things simpler. Then: ...
  • 29.6k
0 votes

Series expansion of the integral from its numerical values

I have no idea whether this approach is mathematically valid, but I'll post it anyway. As suggested in the comments, tabulate your integral and use NonlinearModelFit...
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2 votes
Accepted

Cannot get a ParametricPlot from NDSolve and NIntegrate solution

We can use NumericQ to evaluate integral as follows ...
  • 35.3k
4 votes

Find the inverse of Interpolating function from NDSolve

All of the follwing methods are almost equivalent. It is convience to use NDSolveValue and function names {q, y, h, v, x}. <...
  • 41.8k
2 votes

Find the inverse of Interpolating function from NDSolve

The problem is that you need to extract the correct part of sol in some way. For example,sol[[1, 1, 2, 0]] evaluates as ...
  • 15.2k
4 votes
Accepted

Plot The Magnetization

Function g[k_] := Tr[Eigenvalues[h[k]]] is periodic with a period of 4 Pi, therefore we suppose that integral should be defined ...
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