Runge kutta Definition and 56 Threads

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...

First we need to write the DE as a system of first order DEs. Let $\displaystyle u = y $ and $\displaystyle v = y' $. Then $\displaystyle \begin{align*} x^2\,y'' - 5\,x\,v + 7\,u &= 2\,x^3\ln{\left( x \right) }\\ x^2\,y'' &= 5\,x\,v - 7\,u + 2\,x^3\ln{ \left( x \right) } \\ y'' &=...

You first have to write this DE as a system of first order equations. Note, since $\displaystyle t$ does not appear in the original DE, that means that the system will be autonomous if kept in terms of $\displaystyle t$. Let $\displaystyle y = u$ and $\displaystyle y' = v$, then...

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...

Homework Statement Hi, can someone explain how they get this stability function. Homework Equations http://blob:http://imgur.com/840ee1fe-f09c-49ab-bdbb-7f953777f900 The Attempt at a Solution I have attempted to do it two ways, and I'm not sure if I'm just having an awfully bad day at maths...

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 (tw')' + tw = 0 with w(0) = 1, w'(0) = 0 on the interval [0,1] by introducing the new variable v=tw' and considering the resulting first order differential system involving w and v Report your computed solution (wh(1),vh(1)) for h=1/10. Homework Equations The...

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...

Hello ppl, I'm new here. I'm trying to compute RK4 for N-body problem. But after computing I'm getting strange numbers. So here are the formulas for these problem. Start from two differential equations of first order: [1] d\vec{r}/dt = \vec{v_i} [2] \frac{d\vec{v_i}}{dt} = \gamma...

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...

Hi! If you don't see clearly this n terms please download the word file attached here. Am a given a problem like f(x,y,y')= y''= x+y with y(0)=0, y'(0)=1 and h=0.1 and i want to solve it using Ringe Kutta. As we know y_(n+1)= y_n + h(y'_n+(A_n + B_n + C_n)/3) And y'_(n+1) =...

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.