div, grad, lap extended to periodic bc. All examples tested

div, grad, and lap extended for non-periodic and periodic bc keeping legacy code. All examples in the MOLE were tested successfully

Author: mdumett

examples/matlab/elliptic1DGralPerBC.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u(0) = 0, u(1) = 0
 % exact solution: u(x) = x(1-x)/2
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -22,7 +22,7 @@
 v = [0;0];
 A = - lap(k,m,dx);
 b = ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DHomogeneousDirichlet.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u'(0) = 0, u(1) = 0
 % exact solution: u(x) = (1 - x^2)/2
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -22,7 +22,7 @@
 v = [0;0];
 A = - lap(k,m,dx);
 b = ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftDirichletRightNeumann.m

@@ -9,7 +9,7 @@
 % b = 400, c = 10, d = 15
 % So, E = (pi - 3985)/401, F = 10
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -28,7 +28,7 @@
 v = [10;15];
 A = - lap(k,m,dx);
 b = pi^2 * sin(pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftDirichletRightRobin.m

@@ -5,7 +5,7 @@
 % Compatibility condition: 
 % integ(f) = integ(-u'') = - u'(1) + u'(0) 
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -24,7 +24,7 @@
 v = [0;0];
 A = - lap(k,m,dx);
 b = xc - 0.5*ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution (there are infinity solutions)
 ua = ua - ua(1) + ue(1); % shifting ua to match ue(1) with ua(1)
 

examples/matlab/elliptic1DLeftNeumannRightNeumann.m

@@ -9,7 +9,7 @@
 % b = 400, c = 10, d = 15
 % So, E = - (10 + pi), F = (402 pi + 4025)/400
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -28,7 +28,7 @@
 v = [10;15];
 A = - lap(k,m,dx);
 b = pi^2 * sin(pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftNeumannRightRobin.m

@@ -11,7 +11,7 @@
 % a = -200, b = 400, c = 10, d = 15
 % So, E = (35 - pi)/403, F = (402 pi - 3995)/80600
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -30,7 +30,7 @@
 v = [10;15];
 A = - lap(k,m,dx);
 b = pi^2 * sin(pi*xc);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DLeftRobinRightRobin.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u(0) = 1/2, u(1) = 1/2
 % exact solution: u(x) = (-x^2 + x + 1)/2
 % ===================================================
-% example that uses addBC1D
+% example that uses addScalarBC1D
 %
 close all; clc;
 
@@ -22,7 +22,7 @@
 v = [1/2;1/2];
 A = - lap(k,m,dx);
 b = ones(size(A,2),1);
-[A0,b0] = addBC1D(A,b,k,m,dx,dc,nc,v);
+[A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution
 
 % plot

examples/matlab/elliptic1DNonHomogeneousDirichlet.m

@@ -3,7 +3,7 @@
 % - u'' = 1, 0 < x < 1, u(0) = 0, u(1) = 0
 % exact solution: u(x) = x(1-x)/2
 % ===================================================
-% example that uses lapGral1D
+% example that uses addScalarBC1D with non-periodic boundary conditions
 %
 close all; clc;
 
@@ -20,7 +20,7 @@
 dc = [1;1];
 nc = [0;0];
 v = [0;0];
-A = - lapGral1D(k,m,dx,dc,nc);
+A = - lap(k,m,dx,dc,nc);
 b = ones(size(A,2),1);
 [A0,b0] = addScalarBC1D(A,b,k,m,dx,dc,nc,v);
 ua = A0\b0; % approximate solution