Questions tagged [numerics]

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

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1answer
125 views

NDSolve problem with maxit, ndsz, and impsagpg

I'm trying to solve a system of 24 non-linear differential equations using Implicit RK method. My code works perfectly for simple case, i.e., BB=0, but for non-zero BB, Mathematica gives errors: ...
2
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1answer
260 views

Improvement of code precision using NDSolve for Differential-Algebraic equation

I'm trying to solve a system of 24 non-linear Differential-Algebraic equations (DAE). I'm using the command NDSolve in Mathematica to solve this system, using this command, the error is too much large....
4
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0answers
127 views
+100

Numerical backward induction — Solving sequential Cournot

I'd like to numerically solve a sequential Cournot competition in which supplier 1 moves before supplier 2, then the manufacturer sources from them, and finally sells the item at market clearing price....
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1answer
100 views

WhenEvent how to handle events at the same time and detection order

I need to use WhenEvent inside NDSolve in which events happen simultaneously. I show simple code to better explain my question: ...
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0answers
37 views

Free boundary condition for American Option using Mathematica NDSolveValue

Was wondering if there is a Mathematica example solving the free boundary condition for American Option using NDSolveValue (free boundary condition is continue to hold v.s. early exercise of the ...
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0answers
32 views

Solving for a few roots in the neighborhood of an initial point for an eigen-equation with many roots

I have a system that is described by a complex matrix, $U$, which is a function of two parameters $f, \beta$ (a dispersion eigen-relation in wave physics). We are interested in the solutions ($f,\beta$...
1
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3answers
59 views

How to ask Mathematica to do the given operation for a set of parameters?

I have a set of numbers like this s = {a, b, c, d, e, f, ..., g, h} and I would like to ask Mathematica to do the following operation (to sum the subtractions of ...
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3answers
79 views

Infinite double sum with exclusion

I would like to evaluate the following sum (numerically will suffice): $$ \sum_{m,n=-\infty,(m,n)\neq(0,0)}^{\infty}\frac{1}{m^{4}+n^{4}} $$ I first tried to do $$ \sum_{m,n=1}^{\infty}\frac{1}{m^{4}+...
1
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1answer
61 views

NDSolve needs multiple executions to work and is very slow

I just simulate a system and use an Extended Kalman Filter to estimate the state. Everything works, but I don't understand why I need to execute the Ndsolve command two times before it can run without ...
1
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1answer
75 views

Optimization of second order ODE with more than one parameter

I want to optimize a second order ODE with more than one variable: ...
1
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0answers
43 views

Large and infinite sums evaluated numerically

I am interested to learn when and how Mathematica is able to evaluate large/infinite sums numerically in reasonable time. I have found that it can evaluate $$ \sum_{l=1}^{\infty}e^{il/2}H_{0}^{(1)}(l) ...
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2answers
44 views

Subscript to replaced parameters

I'm trying to manipulate numerical scheme's indexes: $$ T=D-N \\ \frac{T_i^{n+1}-T_i^n}{\Delta t}=\frac{D_i^{n+1}-D_i^n-(N_i^{n+1}-N_i^n)}{\Delta t} $$ But I don't know how to do the transition on the ...
0
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1answer
55 views

Is it possible to ask Mathematica to give all the roots of the given function?

I have this equation $$ 36 \cos \frac{3 x}{4} \cos \frac{27 x}{20} \left(\cos \frac{3 x}{5} +2 \cos \frac{21 x}{10} \right)=0 $$ Is it possible to ask Mathematica to give all the roots of the ...
2
votes
2answers
102 views

NIntegrate results different when using 0 or 0.0

i was trying to compute a convolution numerically, but got unexpected results. In the end i was able to reduce it to the code below. As you can see, the results are different, depending on whether i ...
3
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2answers
326 views

Suggest an irrational number from decimal one

I want to know is there any function in Mathematica that suggests a simple irrational number combination for decimal one? For example, if I give 0.804738 then I get ...
2
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1answer
53 views

Numeric solution of ODEs oscillates strongly and stops halfway?

I tried to reproduce the results of a paper. The differential equations are given by ...
51
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3answers
4k views

Is manual adjustment of AccuracyGoal and PrecisionGoal useless?

This is a problem confusing me for years. AccuracyGoal and PrecisionGoal are two options that I never truly understand and, to ...
0
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1answer
47 views

NSolve missing solutions

I'm having trouble solving the transcendental equation. For some values ​​of bi, NSolve obtains 6 roots, however when changing the value, it obtains 5. Graphing the function clearly shows that the ...
0
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1answer
60 views

How to use parallel computation in mathematica for numerical Integration

I have a multi dimensional integral and I need to integrate it numerically and than plot it over an extra variable for zeta = 0.5. ...
1
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3answers
130 views

How to approximate the harmonic sum $\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$

How to approximate $$\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$$ Where $\overline{H}_n=\sum_{k=1}^n \frac{(-1)^{k-1}}{k}$ is the skew harmonic number. The mathematica ...
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0answers
53 views

Solving these set of equations with complex parameters

For $\{a,b,c\}\in \mathbb{C}$ and $\{\gamma,N\}\in \mathbb{Z}^+$, I have an equation ...
5
votes
3answers
350 views

My evaluation is taking a lot of time

I was evaluating the roots of a transcendental equation, when I noticed that Mathematica never finishes but stays in the running state. The following is the code that I was using: ...
3
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0answers
70 views

Numerical Mixed Partial Derivatives: How to Choose Scale?

For illustration purposes, consider the function $$ f(x, y) = (x - 1)^2 + (y - 1)^2 + \sin[25(x+y)] . $$ The mixed partial derivatives at the origin are $f^{(x,x)}(0,0) = f^{(y,y)}(0,0) = 2$ and $f^{(...
4
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4answers
453 views

Finding the “least” singular solution for NDSolve

I need to solve a ODE for a function $f_\sigma(x)$, where $\sigma$ is a free parameter to tune. All the solutions are supposed to be singular for some value of $x$, except one for a given value $\...
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0answers
56 views

Assumptions for special functions - dirac delta confusion

I wasn't able to express dirac delta function for the below advection-diffusion-reaction function. (Dirac delta term is useless, either a3 = 0.9; or ...
1
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2answers
75 views

Numerical Integration convergence

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4answers
517 views

Find zeros of a transcendental function

Mathematica 10 can not give me solution of this equation ...
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0answers
25 views

Error using ParallelMap to evaluate NIntegrate of numerical derivative ND

I want to evaluate a numerical integration in which the integrand is constructed out of a function f and its derivative f'. <...
0
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1answer
65 views

Diffusion equation with non uniform diffusion constant

I am trying to numerically solve a 3D diffusion type equation with a spatially varying diffusion $\nabla\cdot(K \nabla T)=\partial T/\partial t$ with K a given function of space with different ...
0
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1answer
29 views

Using NSolve with an interporlated function

I have defined the interpolation function below ...
1
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2answers
90 views

How do you overcome recursion limits when using DSolve?

I have the following program to solve for the neutron to baryon ratio during BBN. I've replaced many of the derived values with constants in order to focus on the problem: ...
13
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5answers
988 views

NDSolve DAE with Constraints

I'm trying to make some numerical simulation with NDSolve. I have encountered a few problems. Here is a simplified version of the equations: ...
0
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2answers
37 views

Warning when confluent hypergeometric function HypergeometricU is wrong?

From the definition as an integral (HypergeometricU/details), this function must be positive. However, it gives negative numbers in some cases with no warning of a potential error. For example, In[...
2
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0answers
99 views

NDSolve big system non linear coupled ODE's Method Residual Stiff System

I'm trying to develop a continuous time unscented Kalman filter for a dynamic system inspired to this article: "On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear ...
22
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2answers
2k views

Eisenstein Series in Mathematica?

Mathematica doesn't seem to have built-in tools to deal with the Eisenstein series: $$\begin{align*} E_{2}(\tau)&= 1-24 \sum_{n=1}^{\infty} \frac{n e^{2 \pi i n \tau}}{1-e^{2 \pi i n \tau}}\\ E_{...
3
votes
1answer
152 views

Find an appropriate algorithm for certain type of first order nonlinear PDE

I am trying to solve a first-order nonlinear PDE of the form $$ \partial_t z(t,x) = f(t, x, z(t,x), \partial_x z(t,x)) $$ with the boundary condition $$ z(0,x) = \phi(x) $$ for some finite domain $x \...
83
votes
4answers
42k views

Why round to even integers?

According to the Mathematica help: Round rounds numbers of the form x.5 toward the nearest even integer. For example: Round[{0.5, 1.5, 2.5, 3.5, 4.5}] gives ...
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0answers
31 views

Tolerance issue with MatrixExp

When I use MatrixExp[m,v] to compute, the error given by mathematica is ...
1
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0answers
36 views

Defining general recurrence expression and extracting coefficient

I'm new to Mathematica and I wish to solve a difference equation which is defined by the relation: $y_{i-1}-2y_{i} +y_{i+1} = f(x_i,y_i),\\y_0 = a, y_n = b.$. Where $x_i$ is given for all $i$. I want ...
8
votes
4answers
1k views

ListPlot very large numbers

Suppose we have the following function: NN = 150; W[n1_] := NN!/(n1 ! (NN - n1!)) (1/2)^n1 (1/2)^(NN - n1) Then we can Plot ...
11
votes
2answers
459 views

Numerically solving Helmholtz equation in 2D for a Guitar

Hi I am new to using Mathematica, so am not too confident. I am essentially trying to model vibrations of a guitar sound board for a project. It would be great to get some visualisations of the ...
22
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3answers
9k views
0
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1answer
89 views

Newton's Method plot [closed]

I'm trying to do c. So far I tried, ...
1
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1answer
43 views

NMaximize seems not to work with a plottable function

I am trying to use maximum likelihood for estimating a parameter for a model based on some experimental data. The likelihood function I am trying to maximize calls a number of custom functions I have ...
0
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1answer
31 views

Contradictory results of numerical evaluations of a function

I have the following function: ...
0
votes
1answer
58 views

NDEigensystem does not evaluate

I am trying to obtain the eigenvalue of a certain $4\times 4$ matrix differential operator. The region I consider is a rectangle of size $5\times 200$. At left and right side, I applied the periodic ...
4
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2answers
244 views

How many equilibrium points exist?

Here comes the definition of a simple potential function ...
1
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0answers
35 views

NArgMax solutions' intersection plotted but not solved for

Defining two functions via NArgMax and plotting, there is an intersection and the Plot function works. But trying to solve for ...
1
vote
2answers
123 views

Why can't Mathematica express a minus operation between two decimal numbers with several places? [closed]

A example of the problem. This is a print from mathematica with the demonstration of the issue.

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