differential-equations

问题 I would like to adapt an initial-value-problem (IVP) to a boundary-value-problem (BVP) using scipy.integrate.solve_bvp . A similar question was asked here, but I do not follow everything explained in the answer. The example below regarding the SIR model was taken from this website. Here, the initial condition y0 is taken to be the initial value of S , I , and R at time x0[0] . This system of ODEs is given by the function SIR below, which returns [dS/dt, dI/dt, dR/dt] over the interval from x

问题 I am receiving an error that I have never recognized before. For some background as to what this code is, I am writing a algorithm with Runge-Kutta to solve a second order differential equation (the angle of a pendulum in relation to time). Even as I am typing this I already know there are probably many errors in this. This is part of my final project in my first ever coding course. Any help I can get, in the simplest language possible, could really help! Here is the ERROR code second_order

问题 I am completely new to python or any such programming language. I have some experience with Mathematica. I have a mathematical problem which though Mathematica solves with her own 'Parallelize' methods but leaves the system quite exhausted after using all the cores! I can barely use the machine during the run. Hence, I was looking for some coding alternative and found python kind of easy to learn and implement. So without further ado, let me tell you the mathematical problem and issues with

问题 I'm writing a C++ program to find solutions for first order differential equations for a college assignment. The program starts up and then once I enter the number of iterations to do I get the error message "Euler's method.exe has stopped working". This is my code: #include <functional> #include <vector> using namespace std; double f_r(double x, double r) { return r; } double f_s(double x, double s) { return -x/s; } double eulerstep(const function<double(double,double)>& f, double xsub0,

问题 I am trying to find a way to make this code faster. Nagumo1 is the function that calculates the value of the two derivatives at time t. function x = nagumo(t, y, f) Iapp = f(t); e = 0.1; F = 2/(1+exp(-5*y(1))); n0 = 0; x = zeros(2, 1); z(1) = y(1) - (y(1).^3)/3 - y(2).^2 + Iapp; %z(1) = dV/dt z(2) = e.*(F + n0 - y(2)); %z(2) = dn/dt x = [z(1);z(2)]; end It is a system of differential equations that represents a largely simplified model of neuron. V represents a difference of electric

问题 I have created a vector which concatenates strings of differential equations that are in the correct format to be used be the differeq ode sovler in Julia (i.e, f(du,u,p,t): Combine <- c("du[1] = - 1*0.4545*(u[1]^1) - 1*27000000*(u[4]^1)*(u[1]^1)", "du[2] = - 1*3100000000*(u[2]^1)*(u[4]^1)", "du[3] = - 1*33000*(u[3]^1)*(u[4]^1)", "du[4] =2*0.4545*(u[1]^1) - 1*3100000000*(u[2]^1)*(u[4]^1) - 1*33000*(u[3]^1)*(u[4]^1) - 1*27000000*(u[4]^1)*(u[1]^1) - 1*8500000*(u[4]^1)*(u[5]^1) - 1*390000000*(u

问题 I'm solving a DAE problem with ode15i solver. I have 8 variables and 8 equations, and the system is complex that the only working solver so far is ode15i. I've used the guide: http://se.mathworks.com/help/symbolic/set-up-your-dae-problem.html. However, this guide doesn't help me to solve the problem with a varying input. My system has a time-dependent input, a function. The function itself is quite simple, but the problem is that the time t in DAE system is in symbolic form, and my input

问题 I am building (my first...) MatLab program, it needs to differentiate an equations symbolically and then use this solution many many times (with different numeric inputs). I do not want it to recalculate the symbolic differentiation every time it needs to put in a new set of numeric values. This would probably greatly add to the time taken to run this program (which - given its nature, a numeric optimiser, will probably already be hours). My question is how can I structure my program such

问题 I want to solve this differential equations with the given initial conditions: (3x-1)y''-(3x+2)y'+(6x-8)y=0, y(0)=2, y'(0)=3 the ans should be y=2*exp(2*x)-x*exp(-x) here is my code: def g(y,x): y0 = y[0] y1 = y[1] y2 = (6*x-8)*y0/(3*x-1)+(3*x+2)*y1/(3*x-1) return [y1,y2] init = [2.0, 3.0] x=np.linspace(-2,2,100) sol=spi.odeint(g,init,x) plt.plot(x,sol[:,0]) plt.show() but what I get is different from the answer. what have I done wrong? 回答1: There are several things wrong here. Firstly, your

问题 I am trying to implement the Taylor method for ODEs in MatLab: My code (so far) looks like this... function [x,y] = TaylorEDO(f, a, b, n, y0) % syms t % x = sym('x(t)'); % x(t) % f = (t^2)*x+x*(1-x); h = (b - a)/n; fprime = diff(f); f2prime = diff(fprime); y(0) = y0, for i=1:n T((i-1)*h, y(i-1), n) = double(f((i-1)*h, y(i-1)))+(h/2)*fprime((i-1)*h, y(i-1)) y(i+1) = w(i) + h*T(t(i), y(i), n); I was trying to use symbolic variables, but I don´t know if/when I have to use double. I also tried