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

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9
votes
2answers
182 views

Efficient way to obtain values of a function defined by an Integral

Consider the following equation: $$S(q)=\frac{(4 \pi \rho ) \int r (h(r)-1) \sin (q r) \, dr}{q}$$ I want to numerically obtain values for $S(q)$ given that I have data points representing $h(r)$ ...
0
votes
0answers
42 views

Numerical Error with Matrix operations [duplicate]

A is a 3x3 matrix, b is a 3x1 vector. I try to convert [A|b], a 3x4 matrix, to [I|0]. So the formula is right multiple ...
6
votes
2answers
503 views

A problem about fixed point iteration theory

Description Recently, I have been learning a couse called "Numerical Analysis". The fixed point iteration theory was introducted to solve the ...
1
vote
1answer
126 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
7
votes
1answer
268 views

Fractal dimension of a large networked molecular system

I am trying to determine the fractal dimension of this complex biomolecule (figure attached). Any clues as to how this can be done. In trying to determine this quantity, I wonder how its ...
37
votes
3answers
7k views

Understanding differences between Maple and Mathematica in examples picked by Maplesoft

I am reading the document How Maple Compares to Mathematica. On page 15 there is an example where Mathematica produces wrong results. Does anybody know why? MAPLE: MATHEMATICA: Also on page 17 ...
3
votes
2answers
202 views

Rounding the coeffcients in a polynomial

I have a very large polynomial with Complex Numbers as coefficients. Due to many calculations, there are rounding off errors. I know however by theoretical considerations, that the coefficients are ...
5
votes
1answer
119 views

Determining the range of parameters that yield real values for a certain NIntegrate form

I have specified just one set of $s$ and $g$ values that yields a real value for the NIntegrate below. It is possible that some $s,g$ combination can give rise to ...
2
votes
1answer
73 views

Improving working precision of LegendreP[n,x]? [duplicate]

I was trying to evaluate N[LegendreP[5,0.1]] The cell gives me: N[LegendreP[5,0.1]]=0.178829 However I wanted more ...
2
votes
2answers
330 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
2
votes
1answer
245 views

NDSolve fails for certain choices of parameters and solve range

I'm trying to solve a pair of coupled ODEs with NDSolve. I know roughly what the solution should look like (both should give periodic functions, pi/2 out of phase, the amplitude of which damp towards ...
3
votes
1answer
142 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 ...
11
votes
2answers
644 views

FEM: Nicer Element Shape for Spherical Region

I'm trying to generate a mesh for later use in the Finite Element Method of the DSolve command. It is basically a parallelepiped with a spherical indentation. I'm ...
8
votes
1answer
482 views

Optimizing Monte Carlo simulation of a Pred-Prey model

My assignment and code As part of an assignment for one of my classes, I'm trying to run a "massive" Monte Carlo simulation in Parallel on the follow model: ...
4
votes
1answer
99 views

How to implement something like NMaximize[ NMinimize [ f(x,y) , {x} ], {y} ]?

Title says it all, really. I want to find some set of values for which a function of those values can't be made larger than a certain number, when some other values (on which that function is also ...
6
votes
1answer
217 views

Numerical error in Mathieu functions

Consider the MathieuCharacteristicA function, which is a piecewise function according to the documentation. The discontinuity happens at integer number. ...
3
votes
3answers
190 views

Solving determinant of a Kronecker product of matrices gives a numerical error - why?

I am doing the following steps (code at the end of the post): I start with a 2x2 matrix (smatrix), which is a function of a single variable (u2). I want to set the determinant of this matrix (...
4
votes
1answer
138 views

Bad numerical approximations

I'm trying to do some calculations here, but for some reason Mathematica starts using numerical approximations that are no good for my work. Specifically: ...
4
votes
2answers
249 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 ...
6
votes
3answers
611 views

Numerically integrating a list-valued function [duplicate]

I want to NIntegrate a List valued function foo[x] which is only defined for numerical ...
7
votes
1answer
1k views

How to solve fluid flow problem based on Navier-Stokes equations?

Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ...
8
votes
3answers
201 views

Complex result for Real vectors in VectorAngle

I was expecting a real angle using VectorAngle when passing real valued vectors, but I obtained a complex angle: ...
10
votes
3answers
4k views

how to solve ODE with boundary at infinity

y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ...
1
vote
0answers
268 views

Problem with NDSolve in Mathematica 9 / 10

I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7: ...
2
votes
1answer
243 views

How can I reduce computation time while still obtaining a good approximation for my function?

I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes. I have this function: $J_p=\sum_{m,n=1}^{\infty} \epsilon_{mn}f_{mn}\...
1
vote
1answer
100 views

Whats the most efficient way to solve an equation numericaly (because it has no analitical solution)

So, I think the problem that Im having is simple but, still, Im not sure on how to do it. I have an equation with no analitical solution: $a_1 \sin \left(2 \theta \right)+a_2 \sin \left(2 \phi\right)...
1
vote
1answer
92 views

How to solve the warning problem and obtain real roots without imaginary part?

I am trying to solve a equation with Newton's method via FindRoot, and the codes are: Define the functions: ...
52
votes
3answers
4k views

Numerically solving Helmholtz equation in 2D for arbitrary shapes

I would like to solve the Helmholtz equation with dirichlet boundary conditions in 2 dimensions for an arbitrary shape. (for a qualitative comparison of the eigenstates to periodic orbits in the ...
22
votes
2answers
259 views

BitShiftRight produces incorrect results in Version 10

Bug introduced in 10.0.0 and fixed in 10.0.2 With Mathematica 10 for Mac, BitShiftRight works properly on lists of up to 100000 numbers, but appears to give ...
2
votes
0answers
117 views

How to handle infeasible points in FindRoot?

I am calling FindRoot[f[x,y],{{x,xInit,xMin,xMax},{y,yInit,yMin,yMax}}] where for some points {x,y}, ...
18
votes
1answer
411 views

How can I mend this broken heart?

Try to evaluate the following code: ...
2
votes
1answer
128 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near <...
1
vote
1answer
202 views

Mathematica unable to solve equation numerically while Wolfram|Alpha can

I want to solve the following equation 2 x == Sinh[x] Mathematica is unable to do so ...
2
votes
1answer
121 views

Numerical evaluation of ChebyshevT

When I evaluate the following Chebyshev series of the first kind in two different ways, I get two very different results: ...
3
votes
2answers
510 views

A problem about function N

Toady,I have a problem about N,described as below: For example N[1/3, 5] (* ==> 0.33333*) and ...
0
votes
0answers
167 views

NMinimize gives an obvious wrong value

I'm trying to minimize a function of 2 lists of the same lenght, but for now the first list has one element, the second is constant. Essentialy, this baffles me: ...
1
vote
1answer
79 views

How to make a discretized NMinimize more precise

I am using Mathematica for physics research and I want to minimize a Hamiltonian equation with respect to two variables (I have also discretized the problem). I have a single constraint. When I plot ...
0
votes
1answer
124 views

Find exact value

I want to know exact x'[t] value where z[t]=0 I know approximate x'[t] value is 107 but I cannot find how to find exact x'[t] value ...
4
votes
1answer
724 views

Using NDSolve to solve Equation of Motion in cylindrical coordinates

I have a set of coupled differential equations which represents the equation of motion of a particle in cylindrical coordinates with the following Hamiltonian: $$ H=\frac{1}{2m} \left( p_r^2 + \frac{...
1
vote
1answer
367 views

FindRoot with vector functions

I'm trying to solve a system of non-linear equations with FindRoot, and I get the answer, but also a ...
1
vote
0answers
274 views

Solve set of non-linear equations with least-squares-fitting - constrain results?

I'm trying to solve a set of functions to determine the material properties from a set of measurement values. (To set up this method I just want to fit my model with some already calculated data). My ...
0
votes
1answer
1k views

how to solve second order nonlinear coupled differential equations using NDSolve with hyperbolic function

i have to solve some solitons scattering through this coupled equations. i need to get two different graph, but still the graph did not come out. and also the equations quite complicated containing ...
6
votes
3answers
629 views

RK4 Gravity Simulator

I have the following RK4 solver which splits the two 2nd order ODEs, used to calculate x and y positions under the influence of a gravitating body where $$x''(t)=\frac{G m x(t)}{(x(t)^2+y(t)^2)^{3/2}}$...
2
votes
1answer
417 views

Euler's method for a 2nd order ODE

This is my first post on this site. Also, I'm new to Mathematica. I'm trying to solve my first problem with Mathematica. It's about solving a 2nd order differential equation. I dont have the explicit ...
12
votes
7answers
712 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often it'...
0
votes
1answer
370 views

Solving for the time-evolution operator in a periodically driven system

I am looking at the Hamiltonian $$H(t)=\begin{pmatrix} 0 & e^{i\Omega t}\\ e^{-i\Omega t}& 0\end{pmatrix}$$ I am trying to solve for the unitary operator $U(t,0)=\mathcal{T}\exp(-i\int_0^t ...
0
votes
2answers
486 views

find the real root

I have the following equation: \begin{equation} (y-1)^{b1} - C~~ y~~ \exp(a x)=0 \end{equation} where $a, b$ are real constants, $C$ may be a complex number. I need to find the real solution of the ...
0
votes
1answer
107 views

Numerical vs Symbolic Integration: Loss of precision

I am trying to integrate the following expression over the time interval $0\leq t \leq \text{period}$. ...
1
vote
1answer
1k views

Runge-Kutta 2nd Order ODE Solver

Suppose I have a 2nd order ODE of the form y''(t) = 1/y with y(0) = 0 and y'(0) = 10, and ...