initial commit / add all books

7 files changed, 272 insertions, 0 deletions

diff --git a/845/CH9/EX9.1/Ex9_1.sce b/845/CH9/EX9.1/Ex9_1.sce
new file mode 100755
index 000000000..939a282c2
--- /dev/null
+++ b/845/CH9/EX9.1/Ex9_1.sce
@@ -0,0 +1,2 @@
+// Example 9.1

+// This is an analytical problem and need not be coded.

diff --git a/845/CH9/EX9.2/Ex9_2.sce b/845/CH9/EX9.2/Ex9_2.sce
new file mode 100755
index 000000000..642893b92
--- /dev/null
+++ b/845/CH9/EX9.2/Ex9_2.sce
@@ -0,0 +1,47 @@
+//Example 9.2

+

+clc

+clear

+

+delx = 0.1;

+delt = 0.002;

+xf = 1;

+tf = 0.006;

+x = 0:delx:xf;

+t = 0:delt:tf;

+m = length(x);

+n = length(t);

+lamda = delt/delx^2;

+

+y = zeros(n,m);

+y(1:n,1) = 0;

+y(1:n,m) = 0;

+y(1,1:m) = sin(%pi*x);

+for k = 2:n

+    M1 = zeros(m-2);

+    M2 = zeros(m-2,1);

+    for i = 1:m-2

+        M1(i,i) = 1+2*lamda;

+        if i==1

+            M1(i,i+1) = -lamda;

+            M2(i) = y(k-1,i+1) + lamda*y(k,i);

+        elseif i==m-2

+            M1(i,i-1) = -lamda;

+            M2(i) = y(k-1,i+1) + lamda*y(k,i+2);

+        else

+            M1(i,i+1) = -lamda;

+            M1(i,i-1) = -lamda;

+            M2(i) = y(k-1,i+1);

+        end

+    end

+    y(k,2:m-1) = (M1\M2)';

+end

+y = round(y*10^4)/10^4;

+mprintf("%4s %7s %9s %8s %9s %9s %9s %9s %9s %9s %9s %9s %9s",'n','t','x = 0.0','x = 0.1','x = 0.2','x = 0.3','x = 0.4','x = 0.5','x = 0.6','x = 0.7','x = 0.8','x = 0.9','x = 1.0');

+disp([(0:n-1)' t' y])

+

+disp("At t = 0.006:")

+disp(y(n,1:m),"Computed Solution:")

+Texact = exp(-%pi^2*tf)*sin(%pi*x);

+Texact = round(Texact*10^4)/10^4;

+disp(Texact,"Analytical Solution:")

diff --git a/845/CH9/EX9.3/Ex9_3.sce b/845/CH9/EX9.3/Ex9_3.sce
new file mode 100755
index 000000000..ae53f775f
--- /dev/null
+++ b/845/CH9/EX9.3/Ex9_3.sce
@@ -0,0 +1,42 @@
+//Example 9.3

+

+clc

+clear

+

+delx = 0.1;

+delt = 0.001;

+xf = 0.5;

+tf = 0.003;

+x = 0:delx:xf;

+t = 0:delt:tf;

+m = length(x);

+n = length(t);

+r = delt/delx^2;

+

+T = zeros(m,n);

+T(1:m,1) = 0;

+delTxi = 0;

+delTxf = 1;

+

+for j = 1:n

+    M1 = zeros(m,m);

+    M2 = zeros(m,1);

+    for i = 1:m

+        if i == 1 then

+            M1(i,i) = 1;

+            M1(i,i+1) = -1;

+            M2(i) = -delx * delTxi;

+        elseif  i == m then

+            M1(i,i) = 1;

+            M1(i,i-1) = -1;

+            M2(i) = delx * delTxf;

+        else

+            M1(i,i) = 1;

+            M2(i) = r*T(i+1,j) + (1-2*r) * T(i,j) + r*T(i-1,j);

+        end

+    end

+    T(1:m,j+1) = (M1\M2);

+end

+T = T(:,2:n+1);

+mprintf("%4s %7s %9s %5s %7s %9s %9s %9s",'n','t','x = 0.0','x=0.1','x = 0.2','x = 0.3','x = 0.4','x = 0.5');

+disp([(0:n-1)' t' T'])

diff --git a/845/CH9/EX9.4/Ex9_4.sce b/845/CH9/EX9.4/Ex9_4.sce
new file mode 100755
index 000000000..a50cc5902
--- /dev/null
+++ b/845/CH9/EX9.4/Ex9_4.sce
@@ -0,0 +1,46 @@
+//Example 9.4

+

+clc

+clear

+

+delx = 0.25;

+delt = 1/32;

+xf = 1;

+tf = delt;

+x = 0:delx:xf;

+t = 0:delt:tf;

+m = length(x);

+n = length(t);

+r = delt/delx^2;

+

+

+T = zeros(m,n);

+T(1:m,1) = 1;

+T(1,1:n) = 0;

+T(m,1:n) = 0;

+

+for j = 1:n-1

+    M1 = zeros(m-2,m-2);

+    M2 = zeros(m-2,1);

+    for i = 2:m-1

+        if i == 2 then

+            M1(i-1,i-1)   = -2*(1+r);

+            M1(i-1,i) = r;

+            M2(i-1)     = -(r*T(i+1,j) + 2*(1-r)*T(i,j) + r*T(i-1,j));

+        elseif i == m-1

+            M1(i-1,i-2) = r;

+            M1(i-1,i-1)   = -2*(1+r);

+            M2(i-1)     = -(r*T(i+1,j) + 2*(1-r)*T(i,j) + r*T(i-1,j));

+        else

+            M1(i-1,i-2) = r;

+            M1(i-1,i-1)   = -2*(1+r);

+            M1(i-1,i) = r;

+            M2(i-1)     = -(r*T(i+1,j) + 2*(1-r)*T(i,j) + r*T(i-1,j));

+        end

+    end

+    T(2:m-1,j+1) = (M1\M2);

+end

+T1 = M1\M2;

+for i = 1:length(T1)

+    disp(strcat(["T",string(i)," = ",string(T1(i))]));

+end

diff --git a/845/CH9/EX9.5/Ex9_5.sce b/845/CH9/EX9.5/Ex9_5.sce
new file mode 100755
index 000000000..19884c709
--- /dev/null
+++ b/845/CH9/EX9.5/Ex9_5.sce
@@ -0,0 +1,45 @@
+//Example 9.5

+

+clc

+clear

+

+delx = 1;

+delt = 1.893;

+alpha = 0.132;

+xf = 4;

+tf = delt;

+x = 0:delx:xf;

+t = 0:delt:tf;

+m = length(x);

+n = length(t);

+r = alpha*delt/delx^2;

+r = round(r*10^2)/10^2;

+

+T = zeros(m,n);

+T(1:m,1) = 1000;

+

+for j = 1:n-1

+    M1 = zeros(m,m);

+    M2 = zeros(m,1);

+    for i = 1:m

+        if i == 1 then

+            M1(i,i) = -(2+2.15*r);

+            M1(i,i+1) = 2*r;

+            M2(i) = -(2*r*T(2,j) + (2-2.15*r)*T(1,j) + 21*r);

+    elseif  i == m then

+        M1(i,i) = -(2+1.75*r);

+        M1(i,i-1) = 2*r;

+        M2(i) = -(2*r*T(m-1,j) + (2-1.75*r)*T(m,j) - 35*r);

+        else

+            M1(i,i-1) = r;

+            M1(i,i)   = -2*(1+r);

+            M1(i,i+1) = r;

+            M2(i)     = -(r*T(i+1,j) + 2*(1-r)*T(i,j) + r*T(i-1,j));

+        end

+    end

+    T(1:m,j+1) = (M1\M2);

+end

+disp(M1,"Coefficient Matrix:")

+disp(M2,"Constant Matrix:")

+T = round(T*10^4)/10^4;

+disp(T',"Table:")

diff --git a/845/CH9/EX9.6/Ex9_6.sce b/845/CH9/EX9.6/Ex9_6.sce
new file mode 100755
index 000000000..8da94fe79
--- /dev/null
+++ b/845/CH9/EX9.6/Ex9_6.sce
@@ -0,0 +1,2 @@
+// Example 9.6

+// This is an analytical problem and need not be coded.

diff --git a/845/CH9/EX9.7/Ex9_7.sce b/845/CH9/EX9.7/Ex9_7.sce
new file mode 100755
index 000000000..e5be14367
--- /dev/null
+++ b/845/CH9/EX9.7/Ex9_7.sce
@@ -0,0 +1,88 @@
+//Example 9.7

+

+clc

+clear

+

+h = 2;

+delt = 4;

+tf = 8;

+xf = 8;

+yf = 6;

+x = 0:h:xf;

+y = 0:h:yf;

+t = 0:delt:tf;

+m = length(x);

+n = length(y);

+p = length(t);

+r = delt/h^2;

+r = round(r*10^2)/10^2;

+

+T = 50*ones(n,m);

+T0 = T;

+T(1,1:m) = 110:-10:70;

+T(n,1:m) = 0:10:40;

+T(2:n-1,1) = [65; 25];

+T(2:n-1,m) = [60; 50];

+

+u = (m-2)*(n-2);

+index = [repmat(2:m-1,1,n-2); gsort(repmat(2:n-1,1,m-2))];

+

+M1 = zeros(u,u);

+M2 = zeros(u,1);

+for j = 2:m-1

+    for i = 2:n-1

+        ind = find(index(1,:)== j& index(2,:) == i);

+        if j == 2 then

+            M1(ind,ind) = 1+2*r;

+            M1(ind,ind+1) = -r;

+            M2(ind) = r*T(i,j-1) + r*T0(i-1,j) + (1-2*r)*T0(i,j) + r*T0(i+1,j);

+        elseif j == m-1 then

+            M1(ind,ind-1) = -r;

+            M1(ind,ind) = 1+2*r;

+            M2(ind) = r*T(i,j+1) + r*T0(i-1,j) + (1-2*r)*T0(i,j) + r*T0(i+1,j);

+        else

+            M1(ind,ind-1) = -r;

+            M1(ind,ind) = 1+2*r;

+            M1(ind,ind+1) = -r;

+            M2(ind) = r*T0(i-1,j) + (1-2*r)*T0(i,j) + r*T0(i+1,j);

+        end

+    end

+end

+value = M1\M2;

+value = round(value*10^4)/10^4;

+for i = 1:length(index(1,:))

+    t = index(:,i);

+    T(t(2),t(1)) = value(i);

+end

+disp(T,"At t = 4:")

+T0 = T;

+

+index = gsort(index,'lc','i');

+M1 = zeros(u,u);

+M2 = zeros(u,1);

+for j = 2:m-1

+    for i = 2:n-1

+        ind = find(index(1,:)== j& index(2,:) == i);

+        if i == 2 then

+            M1(ind,ind) = 1+2*r;

+            M1(ind,ind+1) = -r;

+            M2(ind) = r*T(i-1,j) + r*T0(i,j-1) + (1-2*r)*T0(i,j) + r*T0(i,j+1);

+        elseif i == n-1 then

+            M1(ind,ind-1) = -r;

+            M1(ind,ind) = 1+2*r;

+            M2(ind) = r*T(i+1,j) + r*T0(i,j-1) + (1-2*r)*T0(i,j) + r*T0(i,j+1);

+        else

+            M1(ind,ind-1) = -r;

+            M1(ind,ind) = 1+2*r;

+            M1(ind,ind+1) = -r;

+            M2(ind) = + r*T0(i,j-1) + (1-2*r)*T0(i,j) + r*T0(i,j+1);

+        end

+    end

+end

+value = M1\M2;

+value = round(value*10^4)/10^4;

+for i = 1:length(index(1,:))

+    t = index(:,i);

+    T(t(2),t(1)) = value(i);

+end

+disp(T,"At t = 8:")