What is Runge-kutta: Definition and 67 Discussions
In numerical analysis, the Runge–Kutta methods (English: (listen) RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta.
Hi everyone,
I've a little problem with my algorithm.
I have two grids: one for time and the other one for the radius.
I need to evaluate this equation:
\frac{d\beta(r,t)}{dt}=A\beta(r,t)^N
I try solving this with a simple Runge Kutta II method, but I'm not convinced at all that this works...
Homework Statement
I need to write a Matlab program that solves the following:
Use the Runge-Kutta Fehlberg Algorithm with tolerance TOL= 10^(-4) to approximate the solution to the initial-value problem:
y'=(y/t)^2 + y/t, 1<=t<=1.2, y(1)=1, with hmax=0.05 and hmin=0.02.
Homework...
Homework Statement
Consider the system of coupled second-order differential equations
u''-(t+1)(u')^2+2uv-u^3=\cos{t}
2v''+(\sin{t})u'v'-6u=2t+3
with initial conditions u(0)=1, u'(0)=2, v(0)=3, v'(0)=4. Use the second order Runge-Kutta method with h=0.2 and a=2/3, b=1/3, \alpha=\beta=3/2...
Homework Statement
In brief, I am working on a stellar model.
We started with these four equations:
\delta q/\delta x = px^{2}/t
\delta p /\delta x = -pq/tx^{2}
\delta t /\deltax = -Cp^{1.75} / x^{2}t^{8325}
\delta t /\delta x = -2q/5x^{2}
In the model you switch to the 4th...
Hi
As a high school student I was working on an independent project and at last I found final differential equations that I want to integrate them numerically. I read a little bit and found out that Fourth Order Runge-Kutta Method is one of the good methods. By the way could you please help me...
Greetings,
As I am in vacation now there is no way to ask my teacher so I will resort to this forum, I searched and didn't find it on the forum ( hope I haven't skipped anything ) so here goes my question:
For the Runge-Kutta integration methods, I am really puzzled as to what the 'f'...
Hi,
I am stuck on the initial steps of this problem - its been a while since my diff. eq course.
I need to reduce this into a system of three equations then apply a 4th order runge kutta method to solve.
Homework Statement
f'''+f*f''=0
Boundary conditions:
f'(0)=f(0)=0
f'(infinity)=0
A...
Homework Statement
Use the fourth order Runge-Kutta formula to advance the differential equation:
dy/dt = y with y(0)=1 forward one step h. That is find y(h).
Homework Equations
The Attempt at a Solution
The Runge-Kutta formula is:
x(i+1)=x(i)+h/6 [k(1)+2k(2)+2k(3)+k(4)]...
Homework Statement
Hi,
As part of a computing project I'm doing, I need to use a shooting method, to solve a set of differential equations. I have some trial boundary conditions at either end of the equations, and am going to be integrating from each end and varying some parameters until...
I'm familiar with the Runge-Kutta methods for solving ODEs, but recently I've come across a reference to "Runge-Kutter", in which it appears to be used synonamously (unfortunately it's just a reference, the method is not stated explicitly). Is this a common typo, or is there a separate Runge...
I'm trying to find a location in the Internet where I can download (for free) the following paper:
Kjell Gustafsson , "Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods" (Year of Publication: 1991 )
Thanks in advance
:cool:
Hi, I don't know if this is the right forum to adress, but I will try nevertheless
Im solving a simple two-dimensional differential equation:
dx/dt = (-y,x)
which will give a circle when integrating over time.
Now, the problem is that the simple euler scheme seems to be a lot more...
I've been trying to do some simulations using the Euler, improved Euler, and Runge-Kutta methods. My results for the improved Euler and Runge-Kutta are very close to my results with the plain old Euler method. If there is any improvement, it is negligible. This lack of improvement surprises...
Hi,
Could someone please show me how to solve the following simple problem using the Runge-Kutta (RK4) integration method?
A car at t=0 has acceleration 10m/s/s, velocity 0m/s.
How far would the car travel in 10 seconds?
I know this can be solved using the equations of motion (giving...
We have a pendullum in a car, that is being pulled with:
a) constant F force
b) connectec to a spring, with force F = -kx
The physics part is done, and we have 2 differential equations (non-lineer), and we're supposed to write a C program to calculate theta(t) and x(t) from them. We should...
Hi guys.
I was wondering if anyone could help me with this code. I have sucessfully created a program in visual basic that can run a runge-kutta method. However I want to create one in c++, maybe eventually turn it into a .dll when i work out how to create and use them. :smile:
Here is...