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The Matlab function ode45 implements a one-step method that uses two embedded explicit Runge-Kutta methods with convergence orders 4 and 5 for step size control. [ 29 ] The solution can now be plotted, y 1 {\displaystyle y_{1}} as a blue curve and y 2 {\displaystyle y_{2}} as a red curve; the calculated points are marked by small circles:
Matplotlib (portmanteau of MATLAB, plot, and library [3]) is a plotting library for the Python programming language and its numerical mathematics extension NumPy.It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
Anyway, using the homotopy analysis method or harmonic balance, one can derive a frequency response equation in the following form: [9] [5] [() + ()] =. For the parameters of the Duffing equation, the above algebraic equation gives the steady state oscillation amplitude z {\displaystyle z} at a given excitation frequency.
To be able to plot points, one needs to first decide on a point in plane which will be called the origin, and a couple of perpendicular lines, called the x and y axes, as well as a preferred direction on each of the lines. Usually one chooses the x axis pointing right and the y axis pointing up, and these will be named the positive directions ...
Jay-Z is accused in a lawsuit of raping a 13-year-old girl with fellow music mogul Sean “Diddy” Combs. The lawsuit was first filed in October but did not list Jay-Z, whose given name is Shawn ...
For example, a set of points on a line in n-space transforms to a set of polylines in parallel coordinates all intersecting at n − 1 points. For n = 2 this yields a point-line duality pointing out why the mathematical foundations of parallel coordinates are developed in the projective rather than euclidean space. A pair of lines intersects at ...