using runge kutta RK2 on matlab

Task: You have to use this method to solve the following IVP:

An RL circuit has an emf of 5 V, a resistance of 50 Ω, an inductance of 1 H, and no initial

current ( i.e i(1)=0). Find the current in the circuit at any time t.

The formula is:

Ri+L(di/dt)=V

[James Tursa]

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

[Mohamed Ellabban]

% RK2 (runge kutta 2nd order method)

clc

clear all

close all

% y' = 5-50y

f= @(x,y) 5-50*y;

a= 0;

b= 1;

n= 10;

h= (b-a)/n;

y(1)= 0;

i= 0;

for x= a:h:b

i = i+1;

k1 = f(x,y(i));

k2 =f(x+h,y(i)+h*k1);

phi = 0.5*k1 + 0.5*k2;

y(i+1)= y(i)+ h*phi;

end

[Mohamed Ellabban]

i dont know if it correct or no

[Mohamed Ellabban]

[Torsten]

Compare your numerical results with the analytical solution

i(t) = V/R*(1-exp(-R/L*t))

Answer 1

[Torsten]

function main
  f = @(x,y) 5-50*y; 
  a = 0;
  b = 1;
  n = 100;
  h = (b-a)/n;
  y(1) = 0;
  i = 0;
  for x= a:h:b-h
    i = i+1; 
    k1 = f(x,y(i));
    k2 = f(x+h,y(i)+h*k1);
    phi = 0.5*k1 + 0.5*k2; 
    y(i+1)= y(i)+ h*phi;
  end
  x = a:h:b;
  V = 5;
  R = 50;
  L = 1;
  y_ana = V/R*(1-exp(-R/L*x));
  plot(x,[y;y_ana])
end