Runge-Kutta function

derive a Matlab function that receive a Second-order differential equation and step size and initial value from user and solve it with 4th order Runge-Kutta or 2nd order Runge-Kutta which is choosen by user.

[James Tursa]

What have you done so far? What specific problems are you having with your code?

[john smith]

i dont know how to receive the equation and the way to solve it (4th order Runge-Kutta or 2nd order Runge-Kutta)?

Answer 1

[James Tursa]

Here is some code to get you started. It receives a string from the user for a derivative function of x and t and turns it into a function handle that can be used in an RK scheme.

s = input('Input an expression for the derivative of x (it can use t also): ','s');
dx = str2func(['@(t,x)' s]);

Now you have a function handle that calculates the derivative of x. You call it with the current time t and state x: dx(t,x)

E.g., running this code:

Input an expression for the derivative of x (it can use t also): cos(x) + t*x^2
>> dx
dx =
  function_handle with value:
    @(t,x)cos(x)+t*x^2

However, if your derivative function involves variables from the workspace, then you will need to use eval( ) instead because str2func( ) can't see those local variables when it creates the function handle:

    dx = eval(['@(t,x)' s]);

E.g.,

>> a = 5;
>> s = input('Input an expression for the derivative of x (it can use t also): ','s');
Input an expression for the derivative of x (it can use t also): a*cos(x)+t*x^2
>> dx = str2func(['@(t,x)' s]);
>> dx(2,3)
Undefined function or variable 'a'.   <-- str2func didn't work
Error in @(t,x)a*cos(x)+t*x^2 
>> dx = eval(['@(t,x)' s]);
>> dx(2,3)
ans =
   13.0500   <-- eval did work

For the RK4 and RK2 schemes, what has your instructor given you? Surely there must be algorithms for this that were discussed in class.

Answer 2

[Meysam Mahooti]

https://www.mathworks.com/matlabcentral/fileexchange/55430-runge-kutta-4th-order?s_tid=srchtitle