How Do You Solve ODEs with Runge-Kutta in MATLAB?

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  • Thread starter lordtozo
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    Matlab Ode
In summary, the conversation discusses a problem with using runge-kutta in MATLAB to solve ode, and suggests using the ode45 function and treating the X variable as time in simulink for a more accurate result. The speaker also expresses dislike for using simulink.
  • #1
lordtozo
2
0
d(B^2W)/dx = BW

d(B^2W^2)/dx = (W(1-x)^1/n)^-1

more details are found in the attached file

I have a problem and need serious help using runge-kutta in MATLAB to solve ode

please find attached the problem.

I would appreciate it if someone helps me out

Thanks
 

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  • HOW DO I SOLVE THIS USING RUNGE.doc
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  • #2
Try ode45. In console, type
Code: 
help ode45
 
  • #3
Thanks AiRAVATA.

I have already tried that but I get half of my answers to be equal to the solution and the rest having a difference between +1 and +1.5.
 
  • #4
I don't understand. Can you elaborate?
 
  • #5
Use simulink and treat your X variable as time. Then you can use whatever complicated function you want to update. Compute the derivatives and integrate once. Then supply the result as the new X variable to the system.

I hate SIMULINK anyway. But very convenient for such things. Oh by the way, choose a fixed step solver in simulation parameters.
 

Related to How Do You Solve ODEs with Runge-Kutta in MATLAB?

1. What is an ODE and why is it important to solve it in MATLAB?

An ODE (ordinary differential equation) is a mathematical equation that describes the relationship between a function and its derivatives. It is important to solve ODEs in MATLAB because it allows for efficient and accurate computation of solutions, which can be used to model and understand complex systems in science and engineering.

2. What is the Runge-Kutta method and how does it work?

The Runge-Kutta method is a numerical method used to solve ODEs. It works by breaking down the problem into smaller steps and using a series of calculations to approximate the solution at each step. The accuracy of the method can be improved by using smaller step sizes.

3. How do I implement the Runge-Kutta method in MATLAB?

To implement the Runge-Kutta method in MATLAB, you can use the built-in function "ode45" or write your own code using the equations for the specific form of Runge-Kutta you want to use. It is important to understand the algorithm and the specific parameters and equations needed for your ODE before attempting to code it in MATLAB.

4. What are some common challenges when using the Runge-Kutta method in MATLAB?

Some common challenges when using the Runge-Kutta method in MATLAB include selecting appropriate step sizes and tolerances, ensuring convergence of the solution, and handling stiff systems (systems with rapidly changing dynamics). It is important to carefully consider these factors and adjust them accordingly to obtain accurate and efficient solutions.

5. Are there any alternatives to using the Runge-Kutta method in MATLAB for solving ODEs?

Yes, there are various other numerical methods for solving ODEs in MATLAB, such as Euler's method, Heun's method, and the fourth-order Runge-Kutta method. Each method has its own advantages and limitations, so it is important to choose the most appropriate method for your specific ODE problem.

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