Finished most of bonus too

7 files changed, 83 insertions, 56 deletions

diff --git a/Part 3/figures/abs_sin_24_100_tvbc1.png b/Part 3/figures/abs_sin_24_100_tvbc1.png
new file mode 100644
index 0000000..39622e4
--- /dev/null
+++ b/Part 3/figures/abs_sin_24_100_tvbc1.png
diff --git a/Part 3/figures/abs_sin_24_100_tvbc2.png b/Part 3/figures/abs_sin_24_100_tvbc2.png
new file mode 100644
index 0000000..92839f3
--- /dev/null
+++ b/Part 3/figures/abs_sin_24_100_tvbc2.png
diff --git a/Part 3/scripts/finite_script.m b/Part 3/scripts/finite_script.m
index 6d8177c..76c682c 100644
--- a/Part 3/scripts/finite_script.m
+++ b/Part 3/scripts/finite_script.m
@@ -4,10 +4,10 @@
 clear;
 
 % Set the number of samples to take
-N = 24;
+N = 60;
 
 % Set the total time to run
-m = 100;
+m = 300;
 
 % Declare final size of matrix for speed
 res = zeros(N+1, m+1);
@@ -19,24 +19,8 @@ v = 0.25;
 h = 1/N;
 k = h^2 * v;
 
-% Set initial condition to triangle function
-count = 1;
-for i = 0:h:1
-    if i < 0.5
-        res(count, 1) = 2*i;
-    else
-        res(count, 1) = 2-2*i;
-    end
-    count = count + 1;
-end
-
-% Set inital condition to sin function
-% res(:, 1) = sin(2*pi*(0:h:1));
-
-% Set initial condition to abs of sin
-% res(:, 1) = abs(sin(2*pi*(0:h:1)));
-
-
+% Set Initial condition
+res(:, 1) = get_function(N, h, 3);
 
 % Set boundary conditions
 res(1, :) = zeros(1, m+1);
@@ -49,8 +33,14 @@ for c = 1:m
     end
 end
 
-plot(0:h:1, res);
+for i = 1:m+1
+    if rem(i, 10) == 0
+        plot(0:h:1, res(:, i));
+        hold on;
+    end
+end
+hold off;
 xlabel('x');
 ylabel('y');
-title('Plots of 1D Heat equation over time');
+title('Plots of 1D Heat equation over time, bc = abs(sin(2*pi*x))');
 legend('m = 0', 'm = 1', '...', 'm = 99');
\ No newline at end of file
diff --git a/Part 3/scripts/finite_script.m~ b/Part 3/scripts/finite_script.m~
new file mode 100644
index 0000000..b568d1c
--- /dev/null
+++ b/Part 3/scripts/finite_script.m~
@@ -0,0 +1,42 @@
+% This script implements the finite difference method to solve the heat
+% equation
+
+clear;
+
+% Set the number of samples to take
+N = 24;
+
+% Set the total time to run
+m = 100;
+
+% Declare final size of matrix for speed
+res = zeros(N+1, m+1);
+
+% Set v
+v = 0.25;
+
+% Get h and k
+h = 1/N;
+k = h^2 * v;
+
+% Set Initial condition
+res(:, 1) = get_function(h, 3);
+
+% Set boundary conditions
+res(1, :) = abs(sin(2*pi*(0:1/m:1)));
+res(N+1, :) = abs(sin(2*pi*(0:1/m:1)));
+
+% Calculate M+1 and plot it continuously
+for c = 1:m
+    for i = 2:N
+        res(i, c+1) = v * res(i-1, c) + (1-2*v) * res(i, c) + v * res(i+1, c);
+    end
+end
+
+for i = 1:(N/10-10)
+plot(0:h:1, res());
+end
+xlabel('x');
+ylabel('y');
+title('Plots of 1D Heat equation over time, constantly increasing boundary conditions');
+legend('m = 0', 'm = 1', '...', 'm = 99');
\ No newline at end of file
diff --git a/Part 3/scripts/get_function.m b/Part 3/scripts/get_function.m
new file mode 100644
index 0000000..1e1fb8f
--- /dev/null
+++ b/Part 3/scripts/get_function.m
@@ -0,0 +1,22 @@
+function y = get_function(N, h, f)
+
+y = 0:N;
+
+if f == 1
+    count = 1;
+    for i = 0:h:1
+        if i < 0.5
+            y(count, 1) = 2*i;
+        else
+            y(count, 1) = 2-2*i;
+        end
+        count = count + 1;
+    end
+elseif f == 2
+    y = sin(2*pi*(0:h:1));
+else
+    y = abs(sin(2*pi*(0:h:1)));
+end
+
+end
+
diff --git a/Part 3/scripts/get_function.m~ b/Part 3/scripts/get_function.m~
new file mode 100644
index 0000000..769c3c9
--- /dev/null
+++ b/Part 3/scripts/get_function.m~
@@ -0,0 +1,7 @@
+function y = get_function(bc0, bc1, h, f)
+
+if f == 1
+el
+
+end
+
diff --git a/Part 3/scripts/solvetridiag.m b/Part 3/scripts/solvetridiag.m
deleted file mode 100644
index eca7d3f..0000000
--- a/Part 3/scripts/solvetridiag.m
+++ /dev/null
@@ -1,34 +0,0 @@
-function x = solvetridiag(N,a,b,c,vec)
-
-%
-%
-% Use this function to solve a tridiagonal matrix equation
-% of the form: Tx=v;
-%
-% T is a tridiagonal matrix with entries [a, b, c]
-% on the three non-zero diagonals
-%
-% v is the right hand side vector
-%
-% N is the number of equations
-%
-%
-%**************************************************************
-
-    diag=ones(N,1)*b;
-    x=zeros(N,1);
-    
-    for k = 1:N-1
-        p=diag(k);
-        m=a/p;
-        diag(k+1)=diag(k+1)-m*c;
-        vec(k+1)=vec(k+1)-m*vec(k);
-    end
-    
-    x(N)=vec(N)/diag(N);
-    
-    for k = N-1:-1:1
-        x(k)=(vec(k)-c*x(k+1))/diag(k);
-    end
-
-return
\ No newline at end of file