Questions tagged [numerical-integration]
Questions on the use of numerical functions NIntegrate and NDSolve.
3,688 questions
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Problems with integrals involving DiracDeltas
I want to make Mathematica perform the following integral, assuming that:
$$
\int_0^\infty \delta(x)\,\mathrm{d}x = 1
$$
...
- 433
3
votes
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NDSolve: time-dependent Schroedinger equation with source term
I'm trying to solve the following equation:
$$ i\,\partial_{t}\varPhi_{1}(r,t) =-\frac{1}{2}\,\partial_{r}^2\varPhi_{1}(r,t)+\left(-\frac{1}{r}+\frac{1}{r^{2}}+\frac{1}{2}\right)\varPhi_{1}(r,t)-r^{2}...
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Why does my Mathematica implementation of the Fokas method give inaccurate results for this diffusion-type IBVP?
I am trying to compute the solution of a linear diffusion–advection type equation on a finite interval using the Fokas unified transform method. The initial condition and boundary condition are:
$$
...
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NIntegrate error estimates become wrong with Exclusions
Suppose I want to numerically evaluate the integral
NIntegrate[Cos[Sin[x^2]], {x, 0, 40}]
To obtain its error estimate, I used
...
- 1,155
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NIntegrate with many exclusions slow down computation
I am trying to numerically integrate a complicated function f[t1, t2, t3] over $t_1,t_2,t_3 \in [-4,0]$.
The function is piecewise defined, known to have jump ...
- 1,155
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NIntegrate evaluates to non-numerical values, but error disappears for Methods -> Automatic
I’m trying to numerically integrate a complicated function over a 3D implicit region. Schematically, my code has the form ...
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What does "estimate" in NIntegrate::eincr refer to: the full integral or a subregion?
I am evaluating a complicated 3-dimensional integral in Mathematica with NIntegrate.
I use Method -> "GlobalAdaptive" and set MaxErrorIncreases -> 6000.
During the evaluation, ...
- 1,155
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Numerical Integration of Highly Oscillatory Functions with Bessel Kernels
I have met a integral in my research with Bessel Kernels and Hypergeometric functions.
The codes are
...
- 2,420
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Difficulties in plotting this integral for x>150?
I encountered difficulties in representing the numerical integral below int[a,x] for values of x>150 and for ...
- 1,100
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NIntegrate convergence issues with high-order derivatives of an interpolated function
I hope you are doing well. I am modeling a non-uniform beam in COMSOL Multiphysics (a finite element software) to obtain the first mode shape (vertical displacement as a function of the
𝑥-position). ...
- 131
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Computation of the double integral of a kernel function over 3D polygons
I want to use Mathematica to compute some integrals with sufficiently high precision in order to have a reference value for my numerical tests.
My aim is to compute the following
$$
\int_{K_1} \int_{...
- 123
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NIntegrate of Fox H-function via Mellin-Barnes integral gives incorrect results
I'm working with Fox H-functions in my physics problem and wanted to cross-check Mathematica's built-in FoxH function by directly computing the Mellin-Barnes integral. But my numerical integration isn'...
- 31
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How to make ContourPlot3D faster and more accurate for very complicated, cumbersome functions? Any other alternative method?
I have two complicated and long equations $f(x,y,z)=0$ and $g(x,y,z,u)=0$, that I have written a short part of my original functions $f$ and $g$ below (because of the size limit).
My goal is to ...
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Numerically integrate an implicit vector vectorizedly
I want to define a function f[x] and then be able to integrate numerically as a vector - not component by component. The following is my failed attempt:
...
- 173
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Solving a coupled 2nd order differential equation numerically using NDSolve
I would like to solve the following system of differential equations numerically for two one-dimensional functions $R(x)$ and $\phi(x)$:
\begin{eqnarray}
c_1 \left(R''(x) - (\phi'(x))^2 R(x) \right) - ...
- 147