setfun_lap_3d

  SETFUN_LAP_3D  Sets functions and coefficients for lap_3d

    [uex,uexx,uexy,uexz,ff,gam]=setfun_lap_3d

 Output: uex =@(x,y,z)[....] function handle to the expression of exact
               solution
         uexx =@(x,y,z)[....] function handle to the expression of the first 
               x-derivative of the exact solution
         uexy =@(x,y,z)[....] function handle to the expression of the first 
               y-derivative of the exact solution
         uexz =@(x,y,z)[....] function handle to the expression of the first 
               z-derivative of the exact solution
         ff =@(x,y,z)[....] function handle to the expression of function 
              at right hand side
         gam = coefficient of zero-order term (constant >=0)

0001 function [uex,uexx,uexy,uexz,ff,gam]=setfun_lap_3d
0002 %  SETFUN_LAP_3D  Sets functions and coefficients for lap_3d
0003 %
0004 %    [uex,uexx,uexy,uexz,ff,gam]=setfun_lap_3d
0005 %
0006 % Output: uex =@(x,y,z)[....] function handle to the expression of exact
0007 %               solution
0008 %         uexx =@(x,y,z)[....] function handle to the expression of the first
0009 %               x-derivative of the exact solution
0010 %         uexy =@(x,y,z)[....] function handle to the expression of the first
0011 %               y-derivative of the exact solution
0012 %         uexz =@(x,y,z)[....] function handle to the expression of the first
0013 %               z-derivative of the exact solution
0014 %         ff =@(x,y,z)[....] function handle to the expression of function
0015 %              at right hand side
0016 %         gam = coefficient of zero-order term (constant >=0)
0017 %
0018 
0019 %   Written by Paola Gervasio
0020 %   $Date: 2007/04/01$
0021 
0022 
0023 syms  x y z
0024 gam=0;
0025 Uex=(x.^2+y.^3+3*z);% sin(2*pi*x)*cos(2*pi*y)*sin(2*pi*z); % exact solution
0026 Uexx=diff(Uex,x); % first x-derivative of exact solution
0027 Uexy=diff(Uex,y); % first y-derivative of exact solution
0028 Uexz=diff(Uex,z); % first z-derivative of exact solution
0029 Uexx2=diff(Uexx,x); % second x-derivative of exact solution
0030 Uexy2=diff(Uexy,y); % second y-derivative of exact solution
0031 Uexz2=diff(Uexz,z); % second z-derivative of exact solution
0032 Ff=(gam*(Uex)-(Uexx2+Uexy2+Uexz2)); % right hand side
0033 
0034 uex=strrep(char(Uex),'*','.*');
0035 uexx=strrep(char(Uexx),'*','.*');
0036 uexy=strrep(char(Uexy),'*','.*');
0037 uexz=strrep(char(Uexz),'*','.*');
0038 ff=strrep(char(Ff),'*','.*');
0039 
0040 uex=strrep(char(uex),'/','./');
0041 uexx=strrep(char(uexx),'/','./');
0042 uexy=strrep(char(uexy),'/','./');
0043 uexz=strrep(char(uexz),'/','./');
0044 ff=strrep(char(ff),'/','./');
0045 
0046 uex=strrep(char(uex),'^','.^');
0047 uexx=strrep(char(uexx),'^','.^');
0048 uexy=strrep(char(uexy),'^','.^');
0049 uexz=strrep(char(uexz),'^','.^');
0050 ff=strrep(char(ff),'^','.^');
0051 
0052 
0053 uex=@(x,y,z)[eval(uex)];
0054 uexx=@(x,y,z)[eval(uexx)];
0055 uexy=@(x,y,z)[eval(uexy)];
0056 uexz=@(x,y,z)[eval(uexz)];
0057 ff=@(x,y,z)[eval(ff)];
0058