Thread: Explicit Euler method

Hi I want to write a program to solve these 2 ODEs, but I do know how to do it. Please help!

y'_1 = -y_1 + y_2
y'_2 = -100(y_2 - sin t) + cos t

t is from 0 to 1 and with inital value y_1= 1, y_2 = 2.

time step = 0.01

Originally Posted by oxxiissiixxo

Hi I want to write a program to solve these 2 ODEs, but I do know how to do it. Please help!

y'_1 = -y_1 + y_2
y'_2 = -100(y_2 - sin t) + cos t

t is from 0 to 1 and with inital value y_1= 1, y_2 = 2.

time step = 0.01

and what language are you expected to use?

.

If possible, Matlab is prefer, but C is ok i think. Thanks!

Originally Posted by oxxiissiixxo

Hi I want to write a program to solve these 2 ODEs, but I do know how to do it. Please help!

y'_1 = -y_1 + y_2
y'_2 = -100(y_2 - sin t) + cos t

t is from 0 to 1 and with inital value y_1= 1, y_2 = 2.

time step = 0.01

Crude but should work:

Code:

function rv=IODE
  y=[1,2];
  rv=[0,y];
  dt=0.1;
  for t=0:dt:1-dt
      dydt=[y(1)+y(2),-100*(y(2)-sin(t))+cos(t)];
      y=y+dt*dydt;
      rv=[rv;[t+dt,y]];
  end

returns an array each row consists of the time and the y's

.

thanks but I need to use the explicit euler method to solve this system

Originally Posted by oxxiissiixxo

thanks but I need to use the explicit euler method to solve this system

It is explicit, and it is Eulers method. It uses equation 68 from here

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