function r = sine_gordon_residual ( u, uxy )

%*****************************************************************************80
%
%% sine_gordon_residual() evaluates the residual for the Sine-Gordeon PDE.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    01 May 2024
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Daniel Arrigo,
%    Analytical Techniques for Solving Nonlinear Partial Differential Equations,
%    Morgan and Clayfoot, 2019,
%    ISBN: 978 168 173 5351.
%
%  Input:
%
%    real U, UXY: the values of the solution, and its first mixed derivative.
%
%  Output:
%
%    real R, the residual.
%
  r = uxy - sin ( u );

  return
end

