# Questions tagged [numerics]

Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

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### The numerics of FresnelS[]

Bug introduced in 12.1 or earlier and persisting through 12.1.1 or later [CASE:4615361] Note: A worse problem existed in 12.0 for inputs greater than 8 and of ...
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### Discrepancy between the results of NIntegrate with different methods and options

I am trying to perform a numerical integration on a function defined through a sum of exponential terms. The summation is given by: ...
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### Does not evaluate the Integral and a plane plot

I am trying to compute a ContourPlot and a VectorPlot using the following functions: ...
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### Plot of The RiemannSiegelZ Function

I would appreciate your help to visualize the of the following function RiemannSiegelZ[x] with this range. { 18154980120849865 , 18154980120849885 } I tried this: ...
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### Differentiate a numerically defined function

My function is f[a_, b_] := NIntegrate[Sqrt[(Cos[t] - a)^2 + b^2], {t, 0, Pi}] I want to calculate g[1,1] where ...
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### Using Runge Kutta to solve ODE and plotting trajectories in MATLAB [closed]

With the aid of fourth order Runge-Kutta method, solve the competing species model defined by dx/dt=x(2 - 0:4x - 0:3y); x(0) = 4 dy/dt=y(1 - 0:1y - 0:3x); y(0) = 3 where the populations x(t) and y(t) ...
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### Finding the intersection(s) of a 3D parametric surface and a line

I have some 3D parametric curve par and some line line. I want to find parameters u,v and t for the intersection points of par and line. I tried to do that with NSolve in many different ways and ...
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### Numerical integration of MeijerG function with variables

I applied the integration, How to solve the function which is mentioned below. here, 'theta' is the only variable. q13, q1,q2,p,qi1 are all variables will take value from the loop ranges from 0 to 2, ...
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### How o use singular value decomposition function to find the natural frequency and mode shapes

I have a matrix R which is having a dependency on ω, I am interested in finding the natural frequency and mode shapes of this matrix using SVD how to do this?. The regular way is to take the ...
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### Evaluate function at “good” points used by Plot in numerical problems

Plot function with option Mesh->All shows how mathematica evaluates function to make it most optimal for plotting. I'd like to evaluate some physical function in ...
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### Using functions instead of lists in physics numerical problems

I'm using the following code for calculation of reflection and transmission coefficients through square well potential: ...
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### Mathematica vs. MATLAB philosophy [closed]

During a typical (possibly with alcohol mixed) discussion among some academic peers in regards to numeric calculation and general modern use of computers in science and engineering settings, it become ...
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### Some Strange results from MMA and Matlab

Recently I am repeating a numerical discrete Fourier transform. Since this problem is related to a real experiment. So the authors use some complex functions to fit the results. Below formula is the ...
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### How to access and change the state variable values in NDsolve`Iterate?

Essentially I am trying to calculate the Lyapunov exponent the naive way; i.e., using the method described here by Vaggelis_Z. In each pass of the loop over time a new trajectory is spawned by adding ...
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### NDSolve and Explicit Runge-Kutta method [duplicate]

Welcome all, I have a comment to explain how my system solver. My response was to add ...
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### How to read Z == 0. - 0.00162663 W

I am solving a set of three linear equations with four variables and found out the values of X, Y and ...
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### Root finding: Is there no bisection method root finder?

I am trying to find a root to an equation f[k,...]==0 numerically, where k is the variable I am solving for. Using both NSove as ...
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### Problem with NDSolveValue : “The function value {\$Failed} is not a list of numbers with \ dimensions…”

I was having fun modifying a code given to me as an answer to a previous problem here, courtesy of user Alex Trounev (Thank you again), when I encountered a certain error which I had never seen before....
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### Speed up Multidimensional numerical integration

I have the following 9-D integral, where the domain of integration is a nine-dimensional hypercube of unit length. The problem is that Mathematica takes too long to evaluate this. Is there any ...
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### NArgMax plotting partially wrong solution

In the following MWE, NArgMax finds the correct argmax (br1) as a function of the parameter ...
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### Maxima turn out to be false maxima when extremising function locally

In short: I have a 2-D function that gives this plot, where the orange dots are maxima: There are 4 maxima in this plot. Now, I plot the function again in a smaller region, close to these maxima, ...
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### How do I plot this 3-D, double integral?

I have the following function: I need to plot a 3-D with coordinates f (p, q), p and q. I mean, I enter values for p and q, so that the integral of f (p, q) must be a number. This number must be ...
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### Problem with Binomial numerical computation

Using Mathematica 10.4.1.0 I have a problem with Binomial on numerical computations. For example Binomial[2, 1/5] // N correctly returns ...
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### Finding “missing” solutions of differential equation with NDSolve

I was working with NDSolve, and suddenly this question, appeared, so I decide to try something: Define a differential equation: ...
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### Numerical Integration over experimental numbers

I have a large array {x,y,z} sigma = {{x1,y1,z1},{x2,y2,z2}, ......} where z is a function of x,y: z = f(x,y); the function is known only through its numerical ...
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### Inconsistent and oscillatory behavior with formula

I have the following code ...
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### NumericQ slows down the computation in ContourPlot

I am trying to plot the roots of a function f(x,y) using ContourPlot as follows ...
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### Translating pseudocode for the Jacobi algorithm into Mathematica

Here is an image for the Jacobi algorithm. I have almost no knowledge of Mathematica, the textbook does not help. Does not provide examples. The class average is 64%. I just want to be able to ...
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### Break NDSolve when condition is “almost” constant

I'm trying the solve a differential equation using NDSolve, starting at x=0.001. I'd like the solver to stop when the function ...
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### How to run NDSolve over a large range without freezing?

I am trying to solve a set of coupled differential eqns. I need the solution over a large range of the variable t. But the notebook freezes and stops working. ...
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### Global optimisation - Error bound on NMaximize?

Is it possible to obtain an error bound on NMaximize? e.g. convert the number returned by NMaximize into a rigorous upper bound ...