differential-equations

I was looking for a way to draw slope fields in Matlab. Here is what I am looking for: I have an equation dy/dx = f(x,y) or dx/dt = f(x,y) dy/dt = g(x,y) and I want to draw it in a nice way Because the only answer about it here was not answering my question, it took me some time to find how to do this. Also because this is not something I am doing all the time in matlab (most probably till the next time I will need it, I will forget it) I am creating a memo for me how to do this. If you will find it useful, feel free to upvote so here is the equation: dx/dt = x^2-3xy+y dy/dt = -5x+sin(yx) That

I am working on a project (C# and .NET Framework) which requires me to solve some partial differential equations. Are there any specific libraries based on .NET Framework that I could see and make my work simpler? I have worked with MATLAb and solving partial differential equations is very straightforward there. How can I solve this problem? You could solve the problem in MATLAB and use the MATLAB compiler + Builder NE toolbox to create a .NET assembly which links to the rest of your app. Depends on which PDEs you want to solve and how you want to approach them. Every approach that I know of

I am wondering how to export MATLAB function ode45 to python. According to the documentation is should be as follows: MATLAB: [t,y]=ode45(@vdp1,[0 20],[2 0]); Python: import numpy as np def vdp1(t,y): dydt= np.array([y[1], (1-y[0]**2)*y[1]-y[0]]) return dydt import scipy integrate l=scipy.integrate.ode(vdp1([0,20],[2,0])).set_integrator("dopri5") The results are completely different, Matlab returns different dimensions than Python. The interface of integrate.ode is not as intuitive as of a simpler method odeint which, however, does not support choosing an ODE integrator. The main difference is

I am trying to solve a differential equation with Python. In this two system differential equation if the value of first variable ( v ) is more than a threshold (30) it should be reset to another value (-65). Below I put my code. The problem is that the value of first variable after reaching 30 remains constant and won't reset to -65. These equations describe the dynamics of a single neuron. The equations are taken from this website and this PDF file . import numpy as np import matplotlib.pyplot as plt from matplotlib.ticker import FormatStrFormatter from scipy.integrate import odeint plt

Edit: So I found out that NDSolve for ODE is using Runge Kutta to solve the equations. How can I use the Runge Kutta method on my python code to solve the ODE I have below? From my post on text files with float entries , I was able to determine that python and mathematica immediately start diverging with a tolerance of 10 to the negative 6. End Edit For last few hours, I have been trying to figure out why my solutions in Mathematica and Python differ by 5000 something km . I am led to believe one program has a higher error tolerance when simulating over millions of seconds in flight time. My