Runge kutta Definition and 50 Threads

Hello : trying to run mutiple script files on matlab (matlab basic online) but it is giving an error message the files are about runge - kutta method and applying them on a ODEs the 1 script file Lornz : function dy = Lornz(t,y,sigma,beta,rho) % y is the 3 dimentional state vector % y(1)...

Hi, I'm trying to simulate a 3-body problem with a star at the center of reference system and 2 body orbiting around it using Runge Kutta 4. The 2 bodies perturb each other orbits gravitationally, so my ode system is actually a coupled armonic oscillator and I evaluate the solution of both...

Hi everyone. I'm a new member, great to be here:) I have a few questions that I wanted to ask you guys regarding the method by which we implement the Runge-Kutta approximation of Projectile Motion if we should do it using a numerical iterative method with a Spreadsheet like Excel. I have...

So here's my homework question: This is the reference formula along with the Rung-Kutta form with the variables mentioned in the question Here is my attempt so far: Problem is that i am unsure how to expand this to even get going. I tried referencing my text Math Methods by Boas which has...

When conducting numerical methods using 4th Order Runge-Kutta do the physical units have to be maintained? This never occurred to me until I was writing out all the steps in detail when showing someone I work with the method using a simple projectile motion with drag. It had 4th Order time...

Hi PF, initially I would like you to focus on that link https://books.google.com.tr/books?id=Dkp6CwAAQBAJ&pg=PA389&lpg=PA389&dq=runge+kutta+method++is+tvd+proof&source=bl&ots=47ULQDVwcC&sig=e2zjdnXENJ7WxBbrf6hXkSouvLI&hl=tr&sa=X&ved=0ahUKEwjU5Z2XsbXZAhUMCMAKHWpnATQ4ChDoAQhKMAQ#v=onepage&q=runge...

Homework Statement Edit* should say F'(0) = F(0) = 0 Homework Equations I know that I typically need 3 equations for a 3rd order ODE, does this apply if the is no F'? In the picture above are the equations I came up with, am I on the right trail? Lastly I am familiar with RK4, however I have...

Hey guys, I need your help regarding the derivation of the fourth runge kutta scheme. So, I found http://www.ss.ncu.edu.tw/~lyu/lecture_files_en/lyu_NSSP_Notes/Lyu_NSSP_AppendixC.pdf this derivation. Maybe you have a clue what tehy are doing in C.54. So before this they are calculating the...

I am applying a 4th order Runge-Kutta code to solve the following: \begin{equation} \frac {\partial y_1}{\partial t} = y_2 y_3 - C_1 y_1 \end{equation} \begin{equation} \frac {\partial y_2}{\partial t} = y_3y_1 - C_2 y_2 \end{equation} \begin{equation} \frac {\partial y_3}{\partial z} = y_4...

Homework Statement The ordinary differential equation describing shm is d^2x/dt^2=-w^2x where x is the displacement, t is the time and w is the frequency. If x=0 at t=0, the analytical solution is x=Asin(wt), where A is the amplitude. 1) Rewite equation 1 as two first oder ode's suitable for...

I'm trying to plot the solutions of the second order differential equation d^2R/dt^2 = GM/R^2 + Lz^2/R^3. I'm reducing this to a system of first order ODEs and then using RK4 to solve this system. My code is given by function RK4system() Tsim = 10...

I am looking to numerically solve the (complex) Time Domain Ginzburg Landau Equation. I wish to write a python simulator to observe the nucleation of fluxons over a square 2D superconductor domain (eventually 3D, cubic domain). I am using a fourth order Runge Kutta solver for this which I made...

Homework Statement Hi There! MX''=Fn(sin θ - uCos θ ) MZ''=Fn(cos θ + uSin θ ) - Mg Fn,M,θ,u is constant fn/M = 0.866 M = 6000 θ = 30 u = 0.5774 i split my motion equation into 2 individual 1st ode, X' = Vx Z' = Vz Vx'=[fn*(sin θ - uCos θ )]/M Vz'={[fn(cos θ + uSin θ )]/M} - g...

Hello! Right know I'm trying to make an orbit integrator for solving a logarithmic potential with the form: \begin{equation} \Phi= \frac{v_0^2}{2} ln(x^2+ \frac{y^2}{u^2} + r_0^2) \end{equation} where v0, u, and r0 are constants My approach is to use, \begin{equation} \ddot{q} =...

Hi all i want to write a MATLAB code by runge kutta solution for hiemenz equation. F''' + FF'' + 1 - F'^2 = 0 BCs F(0)=F'(0)=0 and F'(inf)=1 I have programmed for RK Fehlberg, RK4 and RK5 method but the results of these three methods are not matching with actual values. In the cod I defined...

Note that the code I am using is Python. Currently, I am attempting to numerically solve the equations of state that give rise to the Chandrasekar limit for a white dwarf star. My code works for a simple harmonic oscillator given the correct equations of motion, but does not compute the correct...

I have a second order differential equation of the form (theta is a function of time): \theta ''=F\left(\theta ,\theta '\right) Turning them to two first order equations I get: \begin{cases} \theta '\:=\omega \\ \omega '=F\left(\theta ,\omega \right) \end{cases} And here's the algorithm...

I am confused on how to use the Runge Kutta method to solve for a relationship between the Chrandrasekhar Mass and radius on the following two equations of state: dx/dr = (-5/3)*(M/r^2)*[sqrt(1+x^2) /x] where x(r=0) = x_c dM/dr = +3*(r^2)*(x^3) where M(r=0) = 0 where M is the mass, r is...

hello all dear please help me can solve this Example By Simulation With matlab

How does one set up the Runge Kutta for \frac {d^2y} {dt} m = b(\frac {dy} {dt} - \frac {dx} {dt}) + k (y-x) ? Set up the substitution variables: a = \frac {d^2y}{dt} v = \frac{dy} {dt} Then what ? Is there a way to get \frac{dx} {dt} out of the equation ? If not, I have to...

Hi, I'm not a bright programmer , but I have to solve the fallowing equations: ##\frac{df}{dt} = \alpha f -\beta f + \theta g - (f+h)f## ##\frac{dg}{dt} = \psi f- \phi g## ##\frac{dh}{dt} = \xi f+ \mu h -\tau h + \epsilon w- (f+h)h## ##\frac{dw}{dt} = \nu h - \chi h## Where ##f(t)## ...

How can I plot the runge kutta 4 stability region? I know on the i axis the max is \(\pm 2\sqrt{2}\). The plot makes a heart type shape. I don't know how to plot it though but would like to.

Homework Statement Need to solve xy''+y'+xy=0 using Runge Kutta on x[1,3] Couldn't find algorythm to solve second order ODE using this method I know how to do 1st order Homework Equations The Attempt at a Solution I know I have to make this equation into 2 first order ODE...

Hi everyone: I have trouble in an assignment I was given. The instructions are to utilize Runge-Kutta order 2 and 4 to determine the period of the comet Halley (perihelion = 0.586 AU and aphelion = 35.1 AU). The period of the orbit is given by Kepler's third law: Period = Sm3/2 where...

From a cubic function where y(0)=1, y(1)=0, and where there is a local max at y(5/13) I created a basic separable differential equation problem. I wanted to analyze how well different ordered Runge Kutta methods works in an interval [0,1]. Here it is: dy/dt=-6(6/13)1/3(y-343/468)2/3 , y(0)=1...

Hi, I am trying to use the Runge-Kutta method for a problem that looks like this: dy/dt= f(u,v,r) where y= r*L I was wondering if dy/dt can be a function of more than 2 independent variables? Also do I need to do some kind of uncoupling of r and L? (I think L can be in a way...

Hi, Hi. I am trying to enter some differential equations into a Runge-Kutta 4th order spreadsheet which requires input in the form y' = ...? My differential equations are in the form : dvx/dt = -FDvx/mv (i.e relate velocity derivative with respect to time to acceleration). Can anyone...

I've written a Runge Kutta algorithm that uses a fixed step size. It works fine for many of my problems dealing with chemical reaction kinetics but I would like to make it faster and more robust by implementing automatic step size adjustments. I have looked at the at the step-doubling...

Homework Statement In aerodynamics, one encounters the following initial value problem for Airy’s equations: y''(x) + xy = 0, y(0) = 1, y'(0) = 0 Using the Runge-Kutta method with h=0.005 and determine values between x=0 and x=10 sufficient to sketch the relationship...

Hi guys I have two points A and B (in 2 dimensions) and want to use runge kutta 4th order to give me points between these two points starting from A __> B (NOT B___> A). How can I choose the initial point then. Cheers,:smile:

Homework Statement Hi everyone, I'm a bit stuck and have been staring at my fortran code all day. For my project this year I'm writing a program to model a spiral galaxy in which gas clouds circulate, collide and produce star formation. I've written code for gravitational acceleration due to...

I just need to know the general form of the 4th order Runge-Kutta method? For two coupled first order linear ODEs. I can not find it specifically written online, I need it to write a program for the structure of white dwarfs stars, but I am okay with the Physics, just I have never used the...

Hello, i have a bit of a problem with uderestanding how exactly we use RK4 method for solving 2nd order ODE. And last conversation with my proffesor only added up to my confiusion. Further more i couldn't find any example dealing with this problem if any1 could provide link explaining this...

Homework Statement h is the timestep Y' = F(Y) Mk,1 = F(Yk) Mk,2 = F(Yk + 0.5*Mk,1) Mk,3 = F(Yk + h*Mk,2) Mk,4 = F(Yk + h*Mk,3) Yk+1 = Yk + (h/6)*(Mk,1 + 4Mk,2 + Mk,4) Show that the local error is of fourth order The Attempt at a Solution I have written down the...

Apologies if this is in the wrong place, but could someone explain to me how I go about converting the sine-gordan equation with 2 double derivatives into one with a single derivative, or how I alter the rung-kutta algorithm to accommodate such a double derivative?

Hey guys, Attempting to write an adaptive step size function into a 4th order runge kutta integrator for basic orbits. The problems (so far) are as follows: 1.) The step size does not seem to change as one would expect if the recursive definition of the StepSize function was working...

Hi, I have got a coupled Differential equation : \ x_1''\ =\ \frac{F_1}{M_1}\ =\ \gamma\cdot{}\left[-\,\frac{M_S}{|\overrightarrow{x_1}|^3}\cdot{}\overrightarrow{x_2}+\frac{M_2}{|\overrightarrow{x_2-x_1}|^3}\cdot{}(\overrightarrow{x_2-x_1})\right] \ x_2''\ =\ \frac{F_2}{M_2}\ =\...

Homework Statement e^(x) + y = dy/dx, [-1,1], y(0) = 1, N = 4. Homework Equations The Attempt at a Solution h = b-a / N = 0.5 x0= 0, y0 =1 x1= 0.5, y1 = 2.472 x2= 1, y2 = 5.433 x3= 1.5, y3= 11.195 x4=2, y4= 22.146 ===================== These were the values I got for the...

Homework Statement apply the runge kutta of order 4 to solve the ode on [-1,1] with n = 5 of (e^x+y)dx-dy=0 Homework Equations The Attempt at a Solution the problems i have done so far gave me an initial condition to find the k values, then to plus them into the formula...i...

Hello All, I need to utilize a Runge Kutta second order approach to solve two coupled first order DE's simultaneously given some initial conditions and a conservation relationship. The DE's are as follows: \frac{dp}{dt} = aq - bp \frac{dq}{dt} = -aq + bp Where a and b are...

I've been browsing the forum, but I haven't found a way to solve this thing, which has been frustrating me for quite a while, I'm trying to develop a simulation of cue formation and propagation on cars on a single lane road, and of course, I have to compute the acceleration of vehicles obeying a...

Hi. I am working on a runge kutta/integral finder. my goal is to make it "exact to the dx", so to speak. im a beginner at c++, so bear with me. the compiler I am using is dev cpp, incase it matters. my main problem was that apparently i can't have a long double array of size greater than...

Im using a C++ class to try and model the motion of a simple pendulum using numerical analysis, at this stage of my implementation I am trying to produce oscillatory output values of theta and v denoting the displacement and velocity of the pendulum of a period of time. I have successfully...

Homework Statement I really am desperate for help on this one. I need to use the runge kutta method to approximate the motion of an electron in the potential below. The T.I.S.E is known, and I have to try and use the runge kutta method to find the wavefunction of the particle. V(x) =...

Hi I am using adaptive stepsize Runge Kutta (order4) method to solve a set of Lotka Volterra system of equations. But I am getting the errors 1) Step size too small 2) Too many steps in the routine Can somebody please help me on this.

can anyone please explain the fourth order runge kutta method in laymans terms. I've to describe in detail for a report.

hi can anyone explain to me how to get the H value for runge kutta second method? I've searched everywhere online but i just don't understand it. if found h = tn - to/n?? i know what value of "to" is but no clue what values to put in for n and tn? thanks

Runge Kutta Method in C++ Please Help Me This is for an RK4 second order equation. I have run this program several times and am getting the incorrect limit for the Sekhar Mass of the White dwarf star. I was wondering if anyone has a suggestion. Ill post my Source here as well. The program...

Hi ! I'm trying to solve the restricted problem of three bodies, where a negligeable mass particule is moving in the gravitationnal field of two heavy objects which are in circular orbit around their common center of mass. this is a plane problem... I describe the mouvment in the mobile...

Hi everyone! Despite I have not too much knowledge of ODE's I'm trying to implement a more or less general 3D physics simulator. By now, the simulator (only kinematics and simple rotations of a body rigid, at the moment) works with euler integrator but I'd like to move to some more...