MATLAB: Shooting Method On Harmonic Equation

harmonic equationintergrationodeshooting method

I'm really new to Matlab, so this may be ridicously easy what I'm about to ask, but bare with me please.
I'm trying to integrate the Harmonic equation y'' +(a^2)*y=0 with a=2.4, with BC y(0)=y'(pi)=0. I'm doing this to try and "shoot" for the actual value of y at y=pi which we obviously can find analytically but I need to get my head around the code so I can apply this to a more complicated problem.
Thanks.

Best Answer

function main
  ydot0_start = 1.0;
  a = 2.4;
  iflag = 0;
  sol = fzero(@(x)fun_shooting(x,a,iflag),ydot0_start);
  iflag = 1;
  y_at_pi = fun_shooting(sol,a,iflag)
end
function res = fun_shooting(x,a,iflag)
  fun_ode = @(t,y)[y(2);-a^2*y(1)];
  tspan = [0,pi];
  y0 = [0;x];
  [t,y] = ode45(fun_ode,tspan,y0);
  if iflag == 0
    res = y(end,2);
  else
    res = y(end,1);
  end
end
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