ex1.m

ode routines in matlab

function [out] = Ex1(x, y, flag)
%
%  Evaluate the right hand side function for the
%  ODE
%                         
%    y_1'(x) =  y_2(x)
%               
%    y_2'(x) =  4*y_1(x) + 3*y_2(x) - 8*exp(x) * cos(2x)
%                
%
%  This system is equivalent to the second order ODE
%
%    z''(x) - 3 z'(x) - 4 z(x) = - 8 exp(x) * cos(2x)
%
%  The exact solution of the system with initial conditions
%
%    y_1(0) =  2 + 10/13             
%    y_2(0) =  3 + 14/13
%
%  is given by
%    y_1(x) =  exp(-x) + exp(4*x) 
%               + 10/13 * exp(x) * cos(2x) + 2/13 * exp(x) * sin(2x)
%               
%    y_2(x) = -exp(-x) + 4 * exp(4*x) 
%               + 14/13 * exp(x) * cos(2x) - 18/13 * exp(x) * sin(2x)
%


switch( flag )
   case '' % return right hand side

       out  = [ y(2);
                4*y(1) + 3*y(2) - 8*exp(x) .* cos(2*x) ];
   
   case 'jacobian' % return Jaacobian of right hand side

       out  = [ 0   1;
                4   3 ];

   otherwise
       error (['Unknown request.'])
end