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Questions tagged [parametric-functions]

Questions about explicit functions expressed in terms of independent variables, i.e. parameters. Including approaches for rewriting functions using different parameterizations.

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How to use a table with two variables as the values for a function with two variables (x and y)? [duplicate]

I'm sorry if this is a dumb question. I am a student and have 0 prior experience with Mathematica or any sort of coding and I have looked at various resources trying to figure it out myself but still ...
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1answer
36 views

Hide details of ParametricFunction

I use ParametricNDSolve to return a particular combination of the (vector) variables, at the end of the integration range. This gives a ...
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1answer
105 views

Vector ParametricNDSolve and FindRoot interaction

This question came out of this question. I have a set of differential equations, written in vector form. I'm only interested in the value of these at the endpoint, and so I use ...
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1answer
49 views

Using ParametricNDSolve to solve a hysteretic ODE (Wolfram Mathematica 10.0)

I am trying to solve an ordinary differential equation using ParametricNDSolve and I want to fit the solution to some data to get the value of the parameter. The problem I have is that the ODE is ...
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1answer
48 views

Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
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114 views

Light beams reflecting from parabola

How can we show the paths of three light beams in Mathematica which bounce back after hitting the parabola, in a single plot? Suppose we have the following code ...
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40 views

ParametricNDSolve many functions and plotting

I don't understand why I don't get the plots : ...
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1answer
45 views

Label curves with corresponding parameter

How can Plotlegend label each curve with the corresponding value of parameter param in the code below? ...
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2answers
102 views

Generate Piecewise ParametricPlot from Graphics

Some Graphics in Mathematica could also be described by functions, in particular by ParametricPlots. For example, take this ...
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2answers
84 views

Why the function ScalingFunctions does not work?

Why highlighted in red and does not work function ScalingFunctions -> {None, "Reverse"} in ParametricPlot? ...
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96 views

Fitting experimental data with a parametric function

How does one use a fitting routine such as NonlinearModelFit with a ParametricFunction? Example below: First let's generate some data: ...
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1answer
72 views

ParametricFunction from ParametricNDSolveValue changes when evaluated?

I am new to using ParametricNDSolveValue (and ParametricFunctions in general), so I am hoping that I have made a simple error. First I set up a system of differential equations: ...
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1answer
59 views

Estimating parameters on system of differential equations

I am looking for some help estimating the parameters of a series of differential equations to assist fitting the experimental data I have collected. The Problem: The equations are based off of the ...
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1answer
64 views

How can I use options for a ParametricPlot3D?

Using this command I can plot three different curves using ParametricPlot3D ParametricPlot3D[{{t x, Sin[t x], 0}, {0 , Sin[t x], t x }, {t x ,Sin[t x], t x }}, {t, 0, Pi}, {x, 0, 4}] However, my ...
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2answers
53 views

How can I plot a function (unidimensional) in a 3D plot

I would like to plot a figure like that using Mathematica. They figure are three plane wave ( cosine or sin ) all share and have the same coordinate origin. As you observe, the waves propagate along ...
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1answer
40 views

Parametric Ito Process

Is it possible to make a parametric ItoProcess ? I'd like to write that equation : ...
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0answers
28 views

Computing the same stochastic ODE many times but with different random seeds

I have this stochastic ODE, where I'm using ParametricNDSolve and WhenEvents : ...
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Discrete variables in ParametricNDSolve [closed]

I'm trying to write a stochastic differential equation, using ParametricNDSolve and WhenEvents : ...
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1answer
34 views

Transforming ParametricFunction in expression depending on the parameter

As a result of solving an ODE system using ParametricNDSolveValue I obtain 4 functions, each of them a ParametricFunction depending on the parameter specified in <...
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2answers
97 views

Plotting a parametric solution from NDSolve

Im trying to animate multiple points around multiple parametric plots which depicts orbital motion of body around a planet. Initial conditons are; ...
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1answer
63 views

How to plot several animations from a parametric plot loop

I have a piece of code which plots parametric functions using for loops. ...
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2answers
68 views

Finding the amplitude of function solved using ParametricNDSolve

I have been trying to find the peaks of a function I have plotted using ParametricNDSolve. I have to find these peaks to calculate the amplitude of all the various waves in the observed output. By ...
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2answers
81 views

Trouble with Calculating Area of Parametric Region

This question stems from an attempt to solve the following question: How to calculate specific area on surface of sphere? First, I parametrize a circular loop: ...
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1answer
43 views

Plot a parametric curve subject to some condition

I have a parametric curve described by $(x(s,t), y(s,t))$ where I would like to consider $-1\leqslant s,t \leqslant 1$ subject to some additional constraint, say $f(s,t) = 0$. I know I could solve for ...
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How to calculate specific area on surface of sphere?

I am trying to calculate the solid angle subtended by arbitrary-shaped loops on a sphere's surface. First, I parametrize circular loops by: $$\theta(t,k_{x0},r) = k_{x_0} + r \cos(t);$$ $$\phi(t,k_{...
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2answers
99 views

How to calculate arbitrary area on surface of sphere?

I am trying to calculate the solid angle subtended by arbitrary-shaped loops on a sphere's surface. First, I parametrize circular loops by: $$\theta(t,k_{x0},r) = k_{x_0} + r \cos(t);$$ $$\phi(t,k_{...
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1answer
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Problems with continously varying Tube radius

Problem I am trying to plot Tubes made from the Tube function with varying radii. At one point there is a discontinuity and the radius of the tube is much ...
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1answer
125 views

Calculating the sum of the lengths and plotting all curves on the same map

I have a curve like below; ParametricPlot[ FromPolarCoordinates[{Exp[(t + 0)*0.5], t}] // Evaluate, {t, 0, Pi - 0}, PlotRange -> All] This curve rotates ...
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88 views

How to evaluate the “Domain” of a Parametric Function?

In a simple example I try to calculate the time the solution x[t] passes a second time x[t]==1. ...
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208 views

Finding the point closest to a parameteric curve produced by a numerical method

Question How can I find the closest point to a parametric curve produced by a numerical method. General Context I have a parametric curve (which I will call $g$) produced from a averaging many ...
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116 views

Model calibration with phase space data

Forgive me if this is answered elsewhere, I am new to Mathematica and this forum and have tried a number of search phrases to no avail. My question is very general but for example, suppose I throw a ...
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2answers
82 views

ParametricPlot table of complex functions in several graphs

Assume that I have a table of complex functions like Clear[p] Clear[M] M = 10; G = Table[Sin[i p] + p I, {i, M}] I want to ParametricPlot them in graphs, each ...
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53 views

Plotting a vector field embedded in a donut

I have the following code ...
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1answer
99 views

numerical solution of nonlinear differential equation : parameter fitting

I want to fit data X-axis and Y-axis are L and P, respectively n'[L,t] == L a - b n[L,t]^2 - c n[t]^3, n[L,0]==0 a,b,c is independent parameters. P value is ...
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ParametricPlot with more than two parameters [closed]

This is a general question, and it actually was already asked before but for a case that was wisely solved (see here). I'm going to give a naive example to be clear: Let us suppose you have three ...
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5answers
261 views

Functional fixed points (ie fixed point of mapping from function space C[0,1] to itself)

I am looking for some tips or guidance as to what machinery in mathematica can help me get at this problem numerically. I am looking for fixed points of a mapping, but the objects in question are ...
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3answers
145 views

Plotting eigenvalue function along a path with correct coloring

This question has multiple parts to it. The setup is that I have a matrix that is a function of two parameters a and b. I wish to plot the eigenvalues of this matrix along a general path in the a-b ...
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3answers
132 views

Plotting an Equation Using ParametricNDSolve

I'm trying to plot the solution of a set of differential equations and see how the solution changes when the value of a certain variable de is changed. The equations have solutions to the values of de ...
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2answers
300 views

Plot on the surface of a Torus

I'm trying to plot a system with a variable (or field) $\theta(x,t)\in[-\pi,\pi]$ which is an angle at every position $x$. The positional argument $x$ itself is a periodic coordinate $x\in[-\pi,\pi]$. ...
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Plotting gradient and newton directions for parametric system of nonlinear ODEs

I have a bucket (system) of chemical kinetics models, a nonlinear dynamical system given by: where kf >= 0 and kr >= 0 are the parameters. The initial conditions are A(0) = B(0) = 1 and C(0) = 0. I'...
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56 views

How to draw a plane with ParametricPlot3D when f(x,y)==0?

I have the same issue (actually I have exactly the same prompt) as the creator of this topic: Draw two planes of Cartesian equation: y=3-x and z=2+x with Plot3D The answer I found there was really ...
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1answer
50 views

How can I optimize plotting the solution to ParametricNDSolve as a function of a range of values of the parameter?

I'm using ParametricNDSolve to find a solution to a set of first order ODEs which have one independent variable, z. The set of initial values contains a function of t. ...
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Polynomial interpolation using Wachspress construction to interpolate color on a quadrilaterial

My questions is how to use Rational Polynomial interpolants to paint the edges of a quadrilateral smoothly using 4 different colors. My tutor has taught this two-variable version of Pade expansion ...
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1answer
66 views

Taking the limit of a parametric function produced by ParametricNDSolveValue

I'm working on a project for hard-sphere scattering, and to solve the for the phase function $\overline{\delta}_l(k,r)$ I use the variable phase equation $$ \frac{d\overline{\delta}_l(r,k)}{dr} = -\...
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1answer
54 views

Drawing evenly spaced arrows and opaque sheet between curves?

I have a question about drawing arrows/sheets between curves. Suppose I have two 3-d parametric curves like shown below: ...
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1answer
72 views

Implicit and Parametric Plot

I am trying to graph the partials of two equations with respect to t, with both equations being implicit. I know I should be getting ellipses with the x-axis as the major axis. ...
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2answers
40 views

Shading between two regions of two separate parametric curves/function

I have two long functions g12 and g14 in terms of g2: ...
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1answer
104 views

Visualize embedded and immersed Klein bottle

Answers at How to visualize a 4-dimensional parametric surface? give functions for producing images of 3D projections of 4D embeddings of the Klein bottle. Is there a way to get such a 3D projection ...
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1answer
82 views

Estimating parameters for pair of differential equations efficiently

I'm trying to estimate the parameters for the following pair of differential equations ...