Questions tagged [numerics]
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
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Discrepancy in eigenvalues [closed]
I need to calculate the eigenvalues of a matrix and the parameters are such that there is a large difference (several orders of magnitude) between the entries. Theoretically, the matrix has only one ...
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1
answer
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Solving a nonlinear integral equation
I wonder if Mathematica can be used to numerically solve the following nonlinear integral equation?
$\lambda^2(t)-\frac{1}{\lambda^4(t)}+\frac{2}{R_0^2} \int_{R_0}^{R_0+u_0t} R \left[\frac{\lambda^...
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Numerical solution for multi-step PDEs
I am trying to numerically solve the following PDEs in MMA (v12.0)
$$\partial_u f(x,u) =
\left\{\begin{matrix}&-a f(x,u) + b \, \partial_x^2 f(x,u), & 0<u<T\\ &r(x;\alpha_1) \, f(...
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Finding local minimum of a 2D potential
I tried to find a local minimum point of a 2D potential U[\[Chi],\[CurlyPhi]] with both FindMinimum and ...
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Why won't NIntegrate just return 0 for a zero integral? [closed]
When evaluating integrals numerically that are extremely close to zero, I just want to Mathematica to return zero instead of an error. (After all, this is numerical, so "close to zero" means ...
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NDSolve overdetermined but I can't see how
Edit: partial answer
This confuses me but it is due to some behaviour of pattern matching which just seems wrong to me.
An example of the behaviour
...
- 21
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45
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Prime sign ` followed by numerical values [duplicate]
Here are 2 lines of the numerical output of Mathematica:
-0.0021055211287945152282575757575757575812.493743372412704 0.0282098170963017582537878787878787878913....
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Inconsistent results between NIntegrate and Integrate
I get these inconsistent results
What is going wrong? Fast oscillating terms? Small exponential factors?
But then, why the result seems to toggle between values 1 and 2, rather than being a real ...
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Solving Burger's equation with NDSolve at large time
I want to solve the following Burger's equation
$$\partial_tu+\partial_x\left(\frac{u^2}{2}\right)=0,~~x\in[0,2\pi],~t>0\\u(x,0)=\frac{1}{3}+\frac{2}{3}\sin(x)$$
with mathematica. Here's my code:
<...
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Nonlinear Schrödinger Equation With Periodically Varying Function
I am trying to solve Equation. 42 from https://labsites.rochester.edu/agrawal/wp-content/uploads/2019/08/paper_2019_03.pdf
The equation I am trying to solve is a nonlinear Schrödinger equation
More ...
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Giving a scalar and vector function to ND solve?
I'm trying to solve a coupled system of ODEs using NDSolve. In this system, one function is a scalar and another is a vector i.e. it contains multiple components. <...
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3
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Is it possible to solve a differential equation with a user-defined variable mesh in NDSolve?
For some differential equations, its solution may evolve to a cusp, for example, singular behavior. One may want to introduce additional mesh points near the cusp to accurately follow the solution ...
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How to import a file with 3 columns of numerical data and visualize it with ListPointPlot3D? [closed]
The file is plain ascii. e.g. 100 rows, each row like "1.23 2.34 3.45".
I'm a complete novice with Mathematica, I assume this will be trivial.
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Numerically solving nonlinear PDE $u_t = G(u,u_y,u_{xy},u_{xx}u_{yy})$ with unbounded initial condition
I am trying to numerically solve some nonlinear partial differential equations similar to the example given below, for which I have been unable to obtain stable numerical solutions due to some ...
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Solving System of six Non-Linear Equations in Six Unknowns
I've been trying to solve the following system of equations using NSolve and the code has been running for close to 24 hours already. Is this normal? Is there a quicker way to solve these equations? ...
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120
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Nonlinear higher-order equation with fractional derivative in 1d
How can I use Mathematica to solve the following higher order and nonlinear fractional equation?
$$\partial_t u(t,x) +\partial_x(u^k(t,x)\partial_x(-\Delta)^su(t,x)) = f(t,x) \quad t >0, \ x \in (\...
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How do I get the following to be in numerical form? [closed]
How to get this to be a numerical result
Here is sample code that produces the same kind of problem; the 10^3 in the square root does not get simplified
...
3
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4
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279
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Numerical_integration
I have this integrand
Clear[IntegrandEq10]; IntegrandEq10[x_,x0_] := (x*Sqrt[((x/x0)^2)*(1 - (1/x0)) - (1 - (1/x))])^(-1)
and I need to solve it numerically. I ...
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Selecting a set of points from a region to maximize the smallest pairwise distance
Suppose, we have a region (say, for simplicity, a unit cube) and a distance function that, given the coordinates of any two points in the region, calculates the distance between them. It is not simply ...
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How to numerically solve an equation
I would like to solve for $r_2$ the following two (independent) equations:
$x_{Min}(a,b,c,r_1,F)=x_{Max}(a,b,c,r_2,F)$ (1)
and
$x_{Min}(a,b,c,r_2,F)=x_{Max}(a,b,c,r_1,F)$ (2)
where $a$, $b$, $c$, $r_1$...
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Solve hyperbolic fractional problem in 1d
Inspired by the solution of a fractional parabolic problem presented in https://mathematica.stackexchange.com/posts/266475/, I wonder if we can also use Mathematica to solve the following fractional ...
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Solve 1d fractional parabolic equations with Mathematica
How can we use Mathematica to solve the following fractional parabolic problem?
$$\partial_t u(t,x) +a(-\Delta)^su(t,x) + bu(t,x)= f(t,x) \quad t >0, \ x \in (\alpha,\beta),\\
u(t,x) = u_c(t,x)\...
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Solve 1d fractional equation with Mathematica
How can we use Mathematica to solve the following fractional elliptic problem?
$$a(-\Delta)^su + bu= f(x) \text{ in } (0,1),\\
u = c \text{ in } \mathbb{R} \setminus (0,1), $$
for $a,b,c\ge0$ and a ...
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66
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Confusion about precision [duplicate]
When I evaluate
x = 1.0000000000000000001 (* Precision of 20 digits *)
Mathematica returns
...
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48
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Solve PDE via Mathematica [closed]
Here is my code,but it did not work, how to solve this equation with numerical method. I donnot know the problem
...
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How to optimize the $L^{2}$ norm in Mathematica for an iteration scheme and How to plot its 3D graph?
Consider the BVP $y^{\prime\prime}(t)=\frac{3}{2}y(t)^{2}$ with boundary conditions $y(0)=4$ and $y(1)=1$. The initial iterate is in this case $x_{0}=4-3t$. The higher iterates are given by the ...
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Nonlinear differential equations - follow- up question
I have never solved numerically differential equations and in an optimal control problem I got this one that I cannot solve: $$1-f’(x)^2+f’(x)(x +1)+f’’(x)-f’’(x)f’(x)-f’’(x)f’(x)^2=f(x)$$
The initial ...
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Compiling functions with unit conversions
I have a numerical function that incorporates many units that I would like to speed up by using Compile. Here is a toy example of what I mean, doing it manually by ...
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Best way to handle numerical integration and power series with large numbers
Due to the fact that almost everything I do in my research is analytic, I am quite unfamiliar with numeric calculus, so I was wondering if anyone could give me some advice on the most efficient way to ...
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121
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How do I NIntegrate solutions to Differential Equations?
How do I use NIntegrate solutions to Differential Equations?
...
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Understanding a machine-underflow error
I am struggling with some puzzling machine-underflow errors that I can't reduce to a form that makes sense to me, and I would like some help understanding what Mathematica is doing and what it is (or ...
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Mathematica doesn't simplify 1.` x
I'm debugging a program that uses polynomials with numerical coefficients and it turns out that mathematica does not simplify 1.` x[1]^2 x[2]^2 to ...
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How to get a function out of NDSolve
I solved a function using NDSolve and got a result. I also have a plot of the function.
Could someone point me in the right direction how I can print the explicit data points and/or generate a fit ...
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Solving numerically Pdes and Odes and Iteration processes
Dears, I have the following equations: $x^{\prime\prime}(t)=\frac{3}{2}x(t)^{2}$ with $x(0)=4$ and $x(1)=1$. The exact solution is $x(t)=\frac{4}{(1+t)^{2}}$. Now the corresponding operator is
$
Px=x+\...
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Syntax Problem In NDSolve with Free Boundaries
I am considering a problem with two free boundaries. When I consider the equation:
...
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Solving a differential equation with Shooting
So I have a differential equation that I do not expect to solve analytically. I have been trying a few numerical methods, most recently shooting, without any luck.
Appologies for showing the equation ...
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119
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Mathematica gives a solution to a differential equation that does not verify it
The equation I want to solve numerically with WolframCloud is:
...
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2
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127
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NMinimize does not reach the minimum
I need to minimize numerically an expression with constraints. The expression also includes a numerical integral (called 'PNoninteract').
The minimization apparently stops prematurely (I know roughly ...
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3
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Is the result given by NSolve sufficiently reliable to claim that there is such a solution for the equation?
I use this code for ContourPlot
...
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How to obtain the most accurate maximum value of the given equation? Changing WorkingPrecision gives different results
I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1.56 <x< 1.6$ and $3<y<\pi$.
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Which result is more reliable in NMaximize in the given code? with `WorkingPrecision` or without it?
I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
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How to calculate the maximum value of $x $ which satisfy the conditions $g(x,y)=0$ and $f(x,y)>1$?
I have two functions $ f(x,y) $ and $ g(x,y) $ over the domains $ 1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which $g(...
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NSolve and FindRoot give a value which is not correct; how can I obtain the exact solution of the given equation? [closed]
I have two functions $ f(x,y) $ and $ g(x,y) $, I use this code
...
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Why the substraction of two big numbers does not yield 0, but taking their quotient yields 1?
I have two series, generated as,
...
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2
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How to use NIntegrate with symbolic parameters? [closed]
I am trying to evaluate an integral that has two symbolic parameters, $x$ and $y$ in it
$$-\int_0^1\frac{\log (u)}{\sqrt{1-u^2}} \exp \left(\frac{2 u}{u+1}xy-\frac{u^2 (x-y)^2}{1-u^2}\right) \; du$$
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One dimensional wave equation -numerical vs analitcal solution? [closed]
Recently I have been experimenting with one dimensional wave equation with Dirichlet boundary conditions. So the problem goes like this:
I found this formulas in: Qiong-Gui Lin "Yet another ...
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1
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192
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Memory use buildup when solving PDE multiple times
Mathematica V 13.0
Mac OS X ARM (64-bit) - MacBook Pro 13" M1 processor
macOS Big Sur 11.6.2
I am solving a PDE numerically and have noticed that memory use keeps piling up if I execute the same ...
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Is it possible to have a plot without any endpoints markers in NumberLinePlot?
I am using this code
...
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Is it possible to change the endpoints marker in NumberLinePlot in the given code?
I use this code
...
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