Questions tagged [numerics]
Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.
1,473
questions
-2
votes
0answers
61 views
Boltzmann Equations [closed]
How to solve a coupled Boltzmann non-linear differential equations that one encounters in cosmology numerically in Mathematica?
For example-
1
vote
1answer
55 views
Can I force `NSum` to sum exactly for many terms? [closed]
Is there a way to have NSum perform an exact term-by-term summation, when the number of terms is finite?
I have a complicated infinite sum in which each term ...
5
votes
0answers
59 views
Computing log-determinant?
Mathematica does-not have a function to compute the log-det of matrix? Naively computing Log[Det[M]] can be numerically unstable.
3
votes
1answer
93 views
Mathematica unable to evaluate function which it can write explicitly in simple form
I have a function $\psi(x,n)$ in mathematica which is quite complicated. However, plugging in $n=0$ gives a simple form. Mathematica knows this (see below), however it is still unable to even evaluate ...
0
votes
0answers
75 views
Solving equations using Implicit-Runge-Kutta method
I am trying to solve the system of equations using Implicit-Runge-Kutta method but mathematica is showing error "NDSolve::ndcf: Repeated convergence test failure at [Tau] == 4.9`; unable to continue."....
2
votes
2answers
53 views
How to use NIntegrate inside FindRoot?
I am trying to use FindRoot on functions that involve NIntegrate, and Mathematica is throwing undesirable errors even when it ...
3
votes
4answers
72 views
RecurrenceTable for systems of linear difference equations
I'm working on a project that involves developing a financial forecasting model. The equations used in the model will largely be linear difference equations (estimated via some form of regression ...
0
votes
0answers
43 views
How to solve this system of coupled differential equations (numerically) [duplicate]
I am trying to solve this system of coupled differential equations,
code: enter link description here
The problem is when I run the code, it appears:
NDSolve::ndode: The equations {True} are not ...
0
votes
0answers
67 views
How to solve numerically this system of coupled differential equations
I am trying to solve this system of coupled differential equations,
...
1
vote
0answers
20 views
Numerical evaluation of derivatives of pair
I have a set of ordered pairs. How can I take calculus action on that like derivative or integration?
$$
N(E) = \{(2, 3), \cdots \} : N=2 , E=3\\
\mathrm dN(E)/\mathrm dE = ?
$$
0
votes
0answers
49 views
gradient of a numerical function
Is there a way other than interpolation to evaluate the numerical differentiation using Mathematica? I have a function A(x,y) and I want to obtain the gradient of this function.
...
0
votes
1answer
104 views
Solving a system of Non-linear equations by Fixed Point method or Newton Raphson method
I have a system of five equations with ten variables, i.e., the radial distance $r$, polar angle $\theta$; four spin vector components ($St, Sr, S\theta, S\phi$) and four momentum components ($Pt, Pr, ...
3
votes
0answers
42 views
Evaluating Lauricella functions of Third kind numerically in Mathematica
Let's consider the Lauricella function of third kind, denote as $F_{C}(a,b;c_1,...,c_n;x_1,...x_n)$ in MathWorld. Is anyone aware of an algorithm that allows to numerically evaluate such a function ...
3
votes
2answers
167 views
How to merge two or more curves smoothly?
I have plotted three curves. For each range of $x$, one of those curves is true. On the other hand, finally, the result must be a unified curve. Is there any command to unify these three curves?
...
0
votes
2answers
40 views
Truncating digits after calculation
I am working on numerical solutions to PDEs. I get some outputs which I then place back into the original equation to check my answers against expected values which are the original inputs. The ...
0
votes
0answers
39 views
1
vote
0answers
78 views
NDSolve issue, potential singularity or stiff system
I have the following parameters, equations, and NDSolve solution set up as such:
...
0
votes
1answer
79 views
Calculate sensitivities of differential algebraic equation
I would like to calculate sensitivities for a DAE. The DAE can be solved in Mathematica by:
...
6
votes
1answer
104 views
Nonlinear differential equation with unknown parameter and integral form boundary condition
I'm trying to solve numerically a non-linear problem in order to determine the velocity field ($U$) and the film thickness ($h$) of a non-Newtonian fluid over an inclined plane. The equations are,
$$\...
1
vote
2answers
110 views
Q: Problem - FullSimplify returns 0, FindRoot returns value & FindInstance requires system abend
The function at issue:
...
7
votes
3answers
266 views
Embedding non-orthogonal vectors in a vector space
Consider unit vectors $|v_i \rangle$ on an $n$ dimensional vector space, which obey the following relation:
$$\langle v_i|v_i \rangle =1 \quad \& \quad |\langle v_i|v_j \rangle| \leq \epsilon, \...
4
votes
1answer
63 views
Using preconditioners efficiently
I am trying to numerically solve a linear system of equations of the form
A x = a
where A is really ill-conditioned and ...
0
votes
1answer
45 views
Solving two equations with logarithmic terms with NSolve
I want to solve the following set of equations for $M$ and $\epsilon$ :
...
1
vote
0answers
60 views
0
votes
1answer
132 views
Solving a Reaction-diffusion system
I'm just a beginner in Mathematica software. I have version 12.
I am looking for a program that will solve a prey-predator system with diffusion. My problem is that I tried a previously posted ...
0
votes
1answer
65 views
Plot a family of solutions of ODE with singularity
In the post Use Mathematica to plot the flow of an ODE with discontinuity, the following ODE with discontinuous coefficient was solved
...
4
votes
1answer
76 views
Solving a transcendental equation with FindRoot and making a contour plot
I have the following functions,
...
2
votes
1answer
40 views
7
votes
1answer
188 views
Nonlinear elasticity PDE in Mathematica 12
Mathematica 12, Windows 10.
I am trying to solve a PDE in one spatial dimension $R$ and time $t$. I need a solution for displacement $r(R,t)$, radial Cauchy stress $T_{RR}(R,t)$, and radial growth $\...
6
votes
1answer
75 views
How to help NDSolveValue handle the addition of another dependent variable in a set of reaction-diffusion equations
I am trying to use NDSolveValue to solve a system of coupled reaction-diffusion equations in a 2D space (technically 3D cylindrical coordinates, but due to radial ...
1
vote
0answers
34 views
Problem with an infinite sum
I need to calculate a coefficient as follows
coef[a_, j_] :=
E^(-a^2/2)
NSum[(a/Sqrt[2])^n 1/Sqrt[((n - j)!) (j!)], {n, j, Infinity}]
This coefficient is an ...
2
votes
2answers
119 views
3
votes
1answer
55 views
About the accuracy of Method -> FiniteElement in NDSolve, version 12.0
In this question, the equation $uu'=\nu u''$, $x\in (-1,1)$, $u(-1)=1+\delta$, $u(1)=-1$, was considered. The question asked about how to solve this differential equation problem in Mathematica. There ...
1
vote
1answer
38 views
Problem when using NMinimize in a RecurrenceTable
I have a problem when I'm trying to use NMinimize in my RecurrenceTable, like in this example :
...
1
vote
2answers
109 views
Draw characteristic lines of ODE $\dot \gamma(t) = \sqrt{|\gamma(t)|}$ and highlight some of them
Consider the ODE $$\dot \gamma(t) = \sqrt{|\gamma(t)|}$$ with initial data $\gamma(0) =x_0 = -c^2$. The solutions of the ODE are not unique because one has $x(t) = -(t/2 - c)^2$ for $0 \le t \le 2c$, ...
0
votes
0answers
21 views
NMaximize scrambles constraints
There have been lots of questions around regarding the issue that NMaximize/NMinimize may give results - or at least evaluate ...
1
vote
0answers
54 views
Getting NSum to go to the right depth in recursive definitions
I wanted to produce some plots of the action of the Gauss shift map on cumulative distribution functions. This means I wanted to plot functions $F_n(x)$, for $0 \leq x \leq 1$, defined by $F_1(x) = x$ ...
2
votes
1answer
121 views
Help in finding a good guesses for ode
This problem solved in 1 by @bbgodfrey. However, when I changed the parameters, the ode becomes very stiff and I did not know which best guess I need to use for y0. ...
3
votes
1answer
137 views
How to solve a matrix PDE and stop solving when solution becomes singular?
My question consists of two parts:
How do I get mathematica to solve a PDE Matrix system and plot the result? See below for the PDE matrix system. (By plot the result I mean plot the region ...
1
vote
1answer
93 views
Use Mathematica to plot the flow of an ODE with discontinuity
How can I use Mathematica to plot the flow of the following ODE in $\mathbb R$?
$$\frac{d}{dt} X(t,x) = \chi_{\{x>0\}}(X(t,x)), t \in [0,T],$$
$X(0,x) = x, x \in \mathbb R$
where $\chi$ denotes ...
3
votes
3answers
194 views
Extracting solutions from ContourPlot
I am dealing with a complicated equation,involving trigonometric expressions, and I would like to solve it numerically (I gave up trying to obtain a closed form solution).
The equation:
...
14
votes
2answers
460 views
Can Mathematica provide a reliable estimate of the numerical error from NDSolve?
In the Details section of the Mathematica documentation for PrecisionGoal, one is told that
Even though you may specify ...
1
vote
1answer
75 views
Numerically solve of a system of PDEs
I am studying the vibrations of a beam which is coupled to piezoelectric strips. This system is described by the following system of DEs:
...
2
votes
1answer
51 views
How to get an equation to take in a list of points
I am trying to solve and plot a vector which is equal to (xi,yi)+gradientf(xi,yi). I solve for the gradient by finding the derivative. I am struggling with how to write/get the function to take in my ...
1
vote
0answers
32 views
Changing machine precision notebook-wide leads to peculiarities
For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting.
The idea is to dynamically create a ...
1
vote
2answers
257 views
Need help in plotting a function with two variables in ODE
The solution of this ODE was given in this link
Here I am asking, if L is a function of tot, g, Z and ...
9
votes
2answers
289 views
How to detect underflow/overflow (post 11.3)?
This old trick used to work before 11.3:
SetSystemOptions["CheckMachineUnderflow" -> True]
But no longer... so how can we explicitly check for this in v12+??
...
3
votes
1answer
61 views
Getting a stable solution for a simple first-order PDE
I have what is in my estimation a pretty simple PDE. It's the Liouville equation for the density of points in phase space with a hyperbolic secant potential. But when I try to solve it with NDSolve, I ...
2
votes
1answer
112 views
Testing the accuracy of numerically computed derivatives - alternative method
So I have asked this question earlier today:
Testing the accuracy of numerically computed derivatives,
This method works well for DifferenceOrder methods but upon reading https://reference.wolfram....
1
vote
2answers
76 views
Testing the accuracy of numerically computed derivatives
I am calculating approximate derivatives by using NDSolve`FiniteDifferenceDerivative, so this works:
...
