# Runge-Kutta function

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john smith on 29 May 2019
Answered: Meysam Mahooti on 28 Jul 2021
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.
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john smith 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)?

James Tursa on 29 May 2019
Edited: James Tursa 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.

Meysam Mahooti on 28 Jul 2021
https://www.mathworks.com/matlabcentral/fileexchange/55430-runge-kutta-4th-order?s_tid=srchtitle

R2018b

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