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

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38 views

Numerical derivative of a function which solves a nonlinear system of ODEs

My dear friends, I want to study a nonlinear system of ODEs and to plot a function and its derivative which is defined from the functions of the system of ODE. The question is how to find the ...
7
votes
2answers
194 views

Derivative of the Dedekind eta function fails to compute with errors I don't understand

When trying to understand better the question Eisenstein Series in Mathematica? I stumbled on the following: issuing Derivative[1][DedekindEta][.11 I] gives ...
1
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1answer
65 views

Error with NDSolve when used for a nonlinear system of PDE's

I am trying to solve the following system of Hamilton-Jacobi PDE's: $ V_1,_t - 0.5 V_1,_x^2/(1 - 0.2x)^2 + V_1,_x(0.1x^2+0.03x+.0.01)/(1 - 0.2x)+0.03(x-0.5)^2-V_1,_x V_2,_x/(1 - 0.2x)^2=0$ $ V_2,_t - ...
3
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1answer
309 views

Numerical Instability?

Current Status Please skip ahead to Update 2: the key questions are now: 1/ Why does Mma generally fail to find the minimum for a well behaved function when the function does not have infinite ...
4
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2answers
124 views

Torus-geometry algebraic equations using Nsolve and Reduce

Somehow a set of naive-looking equations cannot be solved by using NSolve. Mathematica returns a message like this: ...
4
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2answers
79 views

N not behaving in the way I expected it would

I'm trying to use the N function to find the percent error between a function and a rounded value of that function. The code looks something like this. ...
2
votes
1answer
105 views

Is there a good way to check, whether a small value produced numerically is a symbolic zero?

I have a complicated 4x4 matrix and need to know the eigenvalues. I expect a zero eigenvalue for physical reasons. Giving numerical values first gives me an eigenvalue of $\mathcal O(10^{-15})$. Now ...
2
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1answer
105 views

NDSolve with two parameters

I was trying to solve a ODE numerically. It has two parameters (w and z0) which I want to vary. The following code gives an ...
0
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0answers
84 views

Solving a second order ODE numerically

I am trying to solve the following second order linear ODE numerically (for small w, say) y''[x]+ D[f[x],x]/f[x] y'[x]+ w^2/(x^2 f[x])^2 y[x] == 0 where, ...
0
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1answer
231 views

How could I solve this Reaction-Diffusion PDE using mathematica?

I'm modeling a problem with PDEs, So I gotta solve numerically this Reaction-Diffusion Partial Differential Equation $$ \frac{\partial u(t,x,y)}{\partial t}=D\Big( \frac{\partial^{2}u(t,x,y) ...
43
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3answers
13k 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}] ...
3
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0answers
117 views

How can I invert a Laplace transform numerically?

I have a very complicated expression, which I want to transform using the inverse Laplace transform. The built-in function InverseLaplaceTransform doesn't work. ...
1
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0answers
67 views

Heron's Method of Square Root Calculation Issue with Previous Suggestion [closed]

Being interested in limit points, which always seem just a little out of reach for me, I recently came across a previous question and answers concerning Heron's (Babylonian) method for calculating ...
4
votes
1answer
135 views

Derivation of numerical scheme for linear transport equation on a variable stencil

The question is about automatica derivation of coefficients of numerical scheme on a variable stencil. So, lets consider 1d transport equation \begin{equation} (1)\qquad u_t+u_x=0. \end{equation} To ...
6
votes
2answers
549 views

Any ideas on how GeneralMiniMaxApproximation is implemented?

GeneralMiniMaxApproximation is used to construct minimax approximations of parametrically defined functions. I am curious about how ...
1
vote
1answer
793 views

Trying to solve a transcendental equation involving Bessel functions

I've never used Mathematica before and am trying to numerically solve equation (12) from this paper. Ideally I'd be able to find the smallest value of $x_{n\nu}$ for $\exp(-kr\pi)$ close to 1, and ...
1
vote
1answer
78 views

Nonlinear 2nd order ODE with regular singularities

I am tring to solve the following ODE with NDsolve $2x~(1-x)~f''(x)+(3-4x)~f'(x)+a~f(x)+b~f^n(x)=0;~~a,b\in\mathbb{R},~n\in\mathbb{N}$. The mathematica "code" is: ...
0
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2answers
117 views

Strange behavior of Plot over a domain containing very large x-values

When I plot a function of (1 + 1/n)^n,There you can see: Plot[{(1 + 1/n)^n, E}, {n, 1, 10^13}] When I add a option of ...
6
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2answers
222 views

Gamma function computation efficiency?

I wonder what kind of algorithm is used to compute the values for the gamma function. Specifically, I am interested in how the computational load increases when the complexity of the input grows. So, ...
4
votes
3answers
187 views

How to read the intersect corodinate of two lines from the ListLinePlot?

Suppose I have two curves intersect at some point, how can I read the coordinates from the graph, not read by eye, but find it with more precision by computer. For example, here are two lists created ...
4
votes
2answers
245 views

Problem with machine number precision in compiled functions

When I compile a very big function and give it input the function returns error. I realized that this is because the value of the function becomes smaller than the smallest machine number. Is it ...
20
votes
1answer
714 views

How to determine BLAS/LAPACK implementation used internally for numerical matrix operations?

Is there a command which reveals which implementation of BLAS and LAPACK are used in Mathematica's matrix operations such as Eigensystem? I asked a related question ...
3
votes
1answer
120 views

Solving an equation containing an integral in the unknowns

I have an equation of $x$ and $y$, which reads $$ -\alpha^2+\frac{2}{3} \alpha^3+y^2-\frac{2}{3}y^3+x^3f(\frac{y}{x})=0, $$ where $\alpha$ is positive parameter and $f(x)=\int (1-\tanh x) ...
8
votes
2answers
152 views

Erfc Not Returning Results Specified in Documentation

In the documentation for Erfc (under "Possible Issues"), the following command returns a number that is extremely close to 2: However, when I run this same command in a fresh kernel, I get: ...
16
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2answers
276 views

More efficient method to compute moments of the Johnson $S_B$ distribution

Here is a very specific feature request. I need Mean[JohnsonDistribution["SB", γ, δ, 0, 1]] When I issue e.g. ...
6
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2answers
285 views

How to implement a numerically efficient Airy Zeta Function

Define the Airy zeta function for $n=2,3,\dots$, by $$ Z(n) := \sum_r \frac{1}{r^n}. $$ where the sum is over the zeros $r$ of the Airy function $\operatorname{Ai}$. In Mathematica the ...
1
vote
2answers
60 views

Calculating the numerical value of the regularized generalized hypergeometric function

I'm trying to calculate the numerical value of the regularized generalized hypergeometric functions: $\qquad \sf{HypergeometricPFQRegularized}^{(\{1\},\{0,0\},0)}(\{-1.5\},\{-1.,-0.5\},3600.)$ I ...
1
vote
1answer
96 views

How to increase the precision to get the correct roots at the boundaries?

I want to solve an equation and Plot a graph of $\delta(\tau)$, where $0<\tau,\delta<1$. In principal $\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near $\tau=1$ ...
7
votes
1answer
146 views

Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions. In particular, I was initially puzzled by ...
15
votes
2answers
202 views

CompiledFunction returns machine numbers smaller than $MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
5
votes
0answers
64 views

How to pass a custom method to a particular option?

In an answer to my question More efficient method to compute moments of the Johnson $S_B$ distribution, J. M. has come up with a method to compute the moments of the Johnson $S_B$ distribution, which ...
2
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0answers
133 views

How to solve an equation where the unknown variable is inside the integration [closed]

I have an equation: $$ \frac{1}{g}=\int_0^{\frac{1}{\delta}\sinh \frac{1}{g}} \frac{\tanh\left(0.882\, b\,\delta\sqrt{1+z^2}\right)}{\sqrt{1+z^2}}\mathrm{d}z $$ I want to obtain the relation ...
0
votes
0answers
83 views

How to solve boundary value problem with singularities at boundaries?

I have a boundary value problem, solving a system of differential equations with a singular boundary condtion (V[0] = 1/s, s->0) ...
3
votes
1answer
148 views

Strange NSum behavior

If I do: NSum[(i + 1)/(i + 2) LegendreP[i, 0] LegendreP[i, 0], {i, 0, Infinity}] I get: 1.25216 If I do: ...
7
votes
2answers
285 views

Mod[1.2, 0.2] is not equal to zero

Why doesn't the following expression evaluate to zero? In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Edit: This is what I wanted to do: ...
20
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2answers
780 views

Obtain approximate Hessian using FindMinimum

According to the documentation, when FindMinimum is told to use the method "QuasiNewton" on a unconstrained problem, it uses the ...
0
votes
2answers
330 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
3
votes
1answer
97 views

How to make N apply to exponent?

For example, I want to covert y + Sqrt[x] to y + x^0.5, where y and ...
1
vote
2answers
75 views

Need help getting the intercept of two lines in a ContourPlot

I am trying to find a set of parameters $\{\epsilon,\epsilon_b\}$, so that the two local minima have exactly the difference of 15.1 (see code below) and the left sided local minimum and the local ...
2
votes
1answer
91 views

Singularity while solving PDE

I have to solve a PDE (in the context of the functional renormalization group in physics). I have a function of two variables, $U(l,p)$. I know $U(0,p)=U_0(p)$ and then I have an equation (eq925) that ...
3
votes
1answer
138 views

Error when extending 1-dimensional PDE to 2 dimensions

I want to calculate how magnetic flux is trapped in a superconductor near the interface superconductor/vacuum. This problem already was solved analytically by J. Pearl for cylindrical symmetry (if ...
5
votes
3answers
126 views

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 ...
1
vote
1answer
83 views

Limited Precision calculation in Mathematica

I apologize upfront for the simple minded question, however i couldn't find an answer in either the Mathematica documentation or Stack exchange. I am trying to explore the effect of finite precision ...
4
votes
1answer
235 views

Is this a bug of NSum?

Check this: NSum[Log[Abs[m]],{m,1,24}] (*54.7847*) NSum[Log[Abs[m]],{m,1,25}] NSum::nsnum: Summand (or its derivative) (Abs^[Prime])[m]/Abs[m] is not ...
2
votes
3answers
490 views

Plotting a Bifurcation diagram

I have the following system equation v'(t)=2*G*J1[v(t-τ)]cos(w*τ)-v(t) How do you plot the bifurcation diagram, τ in the x ...
2
votes
1answer
224 views

Non-linear curve fit problem

I am having a problem with making a fit to data in Mathematica, which may involve my understanding of the methods available. I am trying to fit the derivative of a Frota function (which is a Single ...
0
votes
0answers
60 views

Use FindRoot to plot function restricted to path through domain

I have a function complex-valued $z(x,y)$ defined on a torus and I have a nice routine which plots paths through $(x,y)$ space satisfying the constraint $\rm{Im}(z)=0$: ...
4
votes
1answer
39 views

Different AccuracyGoal for different variables

Is it possible to set different AccuracyGoals for different variables in numerical commands like FindRoot and NDSolve?
0
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1answer
111 views

How to specify a NeumannValue in a system of non-linear partial differential equations?

I am trying to solve a nonlinear system of partial differential equations. If I assume DirichletConditions it all works well. ...
6
votes
2answers
414 views

Position function not always returning an answer even with no apparent problems

I'm having some problems with Position. Sometimes it will give an empty list instead of the actual position of the element I am looking for when that element is ...