# Questions tagged [numerics]

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

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### Derivative of an interpolation function is noisy

I have a set of numerical data of 1501 points, in the form of $\{x_i,a_i\}$ which I uploaded to here and here. I need to compute the numerical derivative of this data. In particular, I need the ...
255 views

### Newton's Method

Problem statement: I'm currently new to Mathematica and have been trying to solve this problem. I was digging around and found this code: ...
85 views

### How to get solutions for this system of inequalities?

I am new to Mathematica and I am struggling finding the solution for the following problem. I am studying this piecewise function: ...
34 views

### Inverse of Normal Distribution CDF incorrect for large value?

I have a function F which is the CDF of the standard normal distribution. The inverse of F should be infinity at 1. However, I ...
172 views

### On Ж, and the fine-structure constant

I'm trying to reproduce the results from a certain infamous paper that has been moving around the web for the last few days. The details are irrelevant. This paper claims to have a closed-form ...
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### Computing numerically infinite sum of some double series

Let's consider the series: $$F(t) = \sum\limits_{n=0}^{\infty}\sum\limits_{k=0}^{\infty} \frac{(-b)^k(-a)^n\binom{n+k}{k} t^{2n+k(2-\alpha)}}{\Gamma(2n+k(2-\alpha)+2)}$$ where $a,b$ are ...
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### Is it possible to solve following question about integer programming using mathematica?

Consider a $5$-uple $(r,a,b,c,s)$ with $a,b,c\in\mathbb{Z},s\in\mathbb{Q}_+,r\in\mathbb{Z}_+$, denote $\frac{1}{2}(a^2-b^2-c^2)-\frac{s}{r}$ by $\Delta(\mathbf{v})$. Let $A$ be a positive real number....
384 views

### Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
163 views

### Using WhenEvent to Change the Sign of a Constant

I am attempting to change the sign of a constant when a certain condition is met during a numerical integration. Here is the code: ...
135 views

### How to compute many sums or tables efficiently

I have some questions about programming in Mathematica and I would really appreciate it if you could help me. I wish to plot the following function against the variable X, but to do this, first I ...
66 views

### Taking a derivative of an eigenvector

I'm trying to calculate the derivative of an eigenvector that I obtain by ...
91 views

### Help to extend this evaluation!

I'm performing a stochastic evaluation, where i'm interested in the assymptotic behavior of the solutions, but my computer can't stand very large times. So I thought that I could evaluate a certain ...
61 views

### Numerical solution of an ODE using NDSolve

I am to find the solution $R(\rho)$ to the following differential equation, $\frac{\partial}{\partial\rho}\left(A^2\frac{\partial}{\partial\rho}R(\rho)\right)-l(l+1)R(\rho)=0$ where $A$ is a ...
123 views

### How to solve these equations numerically?

I have some differential equations as below. I have tried to solve them numerically with NDSolve: ...
105 views

### Solve PDE by using Spatial Discretization for two dimensional independent spatial coordinates

I have a code given by ...
307 views

### Solving 2D+1 PDE with Pseudospectral in one direction with periodic boundary condition?

According to the documentation about the pseudospectral difference-order: It says: Following the discussion here: I found the messy behavior is always on the artificial boundary in $\omega$-...
59 views

### How can I plot the solutions to this system of non linear ODEs?

I need to solve the following system: $$\left\{ \begin{array} { l l } { (u')^2 + (v')^2 = 1 } \\ {u'v'' - u''v' = uu' + vv' } \end{array} \right.$$ and it's a task that's proven to be quite hard by ...
76 views

### Numerical Inversion of an incomplete beta function expressed as gauss hypergeometric function using Mathematica

I am currently working with this hypergeometric function ${_2}F_1$, $\rho(r)=\frac{2b}{1-q}(1-(\frac{b}{r})^{1-q})^{\frac{1}{2}}{_2}F_1(\frac{1}{2},1-\frac{1}{q-1},\frac{3}{2},1-(\frac{b}{r})^{1-q})$ ...
51 views

### What is the acceptable error in numerical calculations? [closed]

I am doing a calculation where I try to simplify a very complicated complex function. I did this step by step and I checked that the numerical values that the function gets for certain values of the ...
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### Non-linear numerical solution with variable parameter

I have solved the following system non-linear: ...
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### Solve transcendental equation and plot the roots

I am practicing solving the following transcendental equation in Mathematica: ...
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### Handling “ill-conditioned” system of ODE's with NDSolve

I am currently dealing with a system of coupled ODE's which I would like to solve numerically. I have already implemented the system in Mathematica using NDSolve. ...
645 views

### Why changing to float-point value does't improve the speed?

I am testing the first tip of this article Use floating-point numbers if you can, and use them early. I've compared a pair codes and finding it's not helpful to use the float-point number during ...
How does one find eigenvalues $\lambda$ of the following problem? $$\frac{\mathrm{d}^2 u}{\mathrm{d}x^2} = \lambda \left( -u + u^2 \right),$$ $$u(0) = u(1) = 0.$$ Can this be tackled by ...