## Runge-Kutta function

Asked by john smith

### john smith (view profile)

on 29 May 2019
Latest activity Edited by James Tursa

### James Tursa (view profile)

on 29 May 2019
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

### James Tursa (view profile)

on 29 May 2019
What have you done so far? What specific problems are you having with your code?
john smith

### john smith (view profile)

on 29 May 2019
i dont know how to receive the equation and the way to solve it (4th order Runge-Kutta or 2nd order Runge-Kutta)?

### Release

R2018b

Answer by James Tursa

### James Tursa (view profile)

on 29 May 2019
Edited by James Tursa

### James Tursa (view profile)

on 29 May 2019

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.