diff_2d.m

有关the method of line即MOL算法的matlab代码

      function [xz2D]=diff_2D(n1,n2,nD,D,x2D)
%...
%...  A. Vande Wouwer, P. Saucez and W.E. Schiesser (2002)
%...
%...  function diff_2D computes a partial derivative over a two-
%...  dimensional domain using either centered or biased upwind 
%...  approximations. Also, the coding is very simple because it 
%...  uses the corresponding one-dimensional functions.
%...
%...  argument list
%...
%...     n1        number of grid points for the first independent
%...               variable (input)
%...
%...     n2        number of grid points for the second independent
%...               variable (input)
%...
%...     nD        number of the independent variable for which the
%...               partial derivative is to be computed (input)
%...
%...     D         differentiation matrix corresponding to the independent 
%...               variable for which the partial derivative is to be computed 
%...               (input)
%...
%...     x2D       two-dimensional array containing the dependent vari-
%...               able which is to be differentiated with respect to
%...               independent variable nD (input)
%...
%...  the following one-dimensional arrays contain the dependent
%...  variable (x1D) and its partial derivative (xz1D).  in each
%...  case, one of the independent variables is constant and the
%...  other independent variable varies over its total interval.
%...
      if nD == 1,
%...
%...  ******************************************************************
%...
%...  the partial derivative is to be computed with respect to the
%...  first independent variable defined over an interval consisting
%...  of n1 grid points.  
      for j=1:n2,
%...
%...  transfer the dependent variable in the two-dimensional array x2D
%...  to the one-dimensional array u1D so that a differentiation matrix
%...  can be used to calculate the partial derivative
      x1D=x2D(:,j);
%...
%...  compute the partial derivative using the differentiation matrix 
      xz1D=D*x1D;
%...
%...  return the partial derivative in the one-dimensional array uz1D
%...  to the two-dimensional array xz2D
      xz2D(:,j)=xz1D;
%...
%...  the partial derivative at a particular value of the second inde-
%...  pendent variable has been calculated.  Repeat the calculation for
%...  the next value of the second independent variable
      end
%...
      elseif nD == 2
%...
%...  ******************************************************************
%...
%...  the partial derivative is to be computed with respect to the
%...  second independent variable defined over an interval consisting
%...  of n2 grid points.
      for i=1:n1,
%...
%...  transfer the dependent variable in the two-dimensional array x2D
%...  to the one-dimensional array x1D so that a differentiation matrix
%...  can be used to calculate the partial derivative
      x1D=x2D(i,:)';      
%...
%...  compute the partial derivative using the differentiation matrix
      xz1D=D*x1D;
%...
%...  return the partial derivative in the one-dimensional array xz1D
%...  to the two-dimensional array xz2D
      xz2D(i,:)=xz1D';      
%...
%...  the partial derivative at a particular value of the first inde-
% %...  pendent variable has been calculated. Repeat the calculation for
%...  the next value of the first independent variable
      end
%...
%...  the partial derivative has been calculated over the entire n1 x
%...  n2 grid.  therefore return to the calling program with the partial
%...  derivative in the two-dimensional array xz2D
      end