initial commit / add all books

9 files changed, 162 insertions, 0 deletions

diff --git a/964/CH26/EX26.1/26_1.sce b/964/CH26/EX26.1/26_1.sce
new file mode 100755
index 000000000..0af6c6d95
--- /dev/null
+++ b/964/CH26/EX26.1/26_1.sce
@@ -0,0 +1,40 @@
+clc;

+clear;

+function yp=f(t,y)

+    yp=-1000*y+3000-2000*exp(-t)

+endfunction

+y0=0;

+//explicit euler

+h1=0.0005;

+y1(1)=y0;

+count=2;

+t=0:0.0001:0.006

+for i=0:0.0001:0.0059

+    y1(count)=y1(count-1)+f(i,y1(count-1))*h1

+    count=count+1;

+end

+plot(t,y1)

+h2=0.0015;

+y2(1)=y0;

+count=2;

+t=0:0.0001:0.006

+for i=0:0.0001:0.0059

+    y2(count)=y2(count-1)+f(i,y2(count-1))*h2

+    count=count+1;

+end

+plot(t,y2,'.-')

+xtitle("y vs t","t","y")

+h=legend(["h-0.0005","h=0.0015"])

+clf();

+//implicit order

+h3=0.05;

+y3(1)=y0;

+count=2;

+t=0:0.01:0.4

+for j=0:0.01:0.39

+    y3(count)=(y3(count-1)+3000*h3-2000*h3*exp(-(j+0.01)))/(1+1000*h3)

+    count=count+1;

+end

+

+plot(t,y3)

+xtitle("y vs t","t","y")

diff --git a/964/CH26/EX26.1/26_1_1.jpeg b/964/CH26/EX26.1/26_1_1.jpeg
new file mode 100755
index 000000000..29a2401f8
--- /dev/null
+++ b/964/CH26/EX26.1/26_1_1.jpeg
diff --git a/964/CH26/EX26.1/26_1_2.jpeg b/964/CH26/EX26.1/26_1_2.jpeg
new file mode 100755
index 000000000..33d1479ac
--- /dev/null
+++ b/964/CH26/EX26.1/26_1_2.jpeg
diff --git a/964/CH26/EX26.2/26_2.sce b/964/CH26/EX26.2/26_2.sce
new file mode 100755
index 000000000..dd56f99ff
--- /dev/null
+++ b/964/CH26/EX26.2/26_2.sce
@@ -0,0 +1,18 @@
+//clc()

+disp("f(x,y) = 4*exp(0.8*x) - 0.5*y")

+//f'(x,y) = 4*exp(0.8*x) - 0.5*y

+h = 1;

+x=0:h:4;

+y(1) = 2;

+x1 = -1;

+y1 = -0.3929953;

+y10 = y1 + (4*exp(0.8*x(1)) - 0.5*y(1))*2;

+y11 = y(1) + (4*exp(0.8*x(1)) - 0.5*y(1) + 4*exp(0.8*x(2)) - 0.5*y10)*h/2;

+y12 = y(1) + (3 + 4*exp(0.8*x(2)) - 0.5*y11)*h/2;

+t = 6.360865;

+y20 = y(1) + (4*exp(0.8*x(2)) - 0.5*t) *2;

+y21 = t + (4*exp(0.8*x(2)) - 0.5*t + 4*exp(0.8*x(3)) - 0.5*y20)*h/2;

+disp(y21,"the first corrector yields y = ")

+t = 14.84392

+e = (t - y21)*100/t;

+disp("%",e,"error = ")

diff --git a/964/CH26/EX26.3/26_3.sce b/964/CH26/EX26.3/26_3.sce
new file mode 100755
index 000000000..b72953d08
--- /dev/null
+++ b/964/CH26/EX26.3/26_3.sce
@@ -0,0 +1,17 @@
+//clc()

+x1 = 1;

+x2 = 2;

+y1 = 6.194631;

+y2 = 14.84392;

+y10 = 5.607005;

+y11 = 6.360865;

+y20 = 13.44346;

+y21 = 15.30224;

+Ec1 = -(y11 - y10)/5;

+disp(Ec1,"Ec (x = 1) = ")

+e1 = y1 - y11;

+disp(e1,"true error (x = 1) = ")

+Ec2 = -(y21 - y20)/5;

+disp(Ec2,"Ec (x = 2) = ")

+e2 = y2 - y21;

+disp(e2,"true error (x = 2) = ")

diff --git a/964/CH26/EX26.4/26_4.sce b/964/CH26/EX26.4/26_4.sce
new file mode 100755
index 000000000..f4ef8ffa2
--- /dev/null
+++ b/964/CH26/EX26.4/26_4.sce
@@ -0,0 +1,26 @@
+//clc()

+//clc()

+x0 = 0;

+x1 = 1;

+x2 = 2;

+y1 = 6.194631;

+y2 = 14.84392;

+y10 = 5.607005;

+y11 = 6.360865;

+y1m = y11 - (y11 - y10)/5;

+e = (y1 - y1m)*100/y1;

+disp(y1m,"ym")

+disp("%",e,"error = ")

+y20 =2+(4*exp(0.8*x1) - 0.5*y1m)*2;

+e2 = (y2 - y20)*100/y2;

+disp(y20,"y20 = ")

+disp("%",e2,"error = ")

+y2o = y20 + 4* (y11 - y10)/5;

+e2 = (y2 - y2o)*100/y2;

+disp(y2o,"y20 = ")

+disp("%",e2,"error = ")

+y21 = 15.21178;

+y23 = y21 - (y21 - y20)/5;

+disp(y23,"y2 = ")

+e3 = (y2 - y23)*100/y2;

+disp("%",e3,"error = ")

diff --git a/964/CH26/EX26.5/26_5.sce b/964/CH26/EX26.5/26_5.sce
new file mode 100755
index 000000000..2c4614273
--- /dev/null
+++ b/964/CH26/EX26.5/26_5.sce
@@ -0,0 +1,17 @@
+//clc()

+disp("f(x,y) = 4*exp(0.8*x) - 0.5*y")

+//f'(x,y) = 4*exp(0.8*x) - 0.5*y

+h = 1;

+x = -3:h:4;

+y(1) = -4.547302;

+y(2) = -2.306160;

+y(3) = -0.3929953;

+y(4) = 2;

+y1(4) = 2;

+for  i = 4:7;

+    y(i+1) = y(i-3) + 4*h*(2*(4*exp(0.8*x(i)) - 0.5*y(i)) - 4*exp(0.8*x(i-1)) + 0.5*y(i-1) + 2*(4*exp(0.8*x(i-2)) - 0.5*y(i-2)))/3;

+    y1(i+1) = y(i-1) + h*(4*exp(0.8*x(i-1)) - 0.5*y(i-1) +4 * (4*exp(0.8*x(i)) - 0.5*y(i)) + 4*exp(0.8*x(i+1)) - 0.5*y(i+1))/3;

+end

+disp(x(4:8),"x = ")

+disp(y(4:8),"y0 = ")

+disp(y1(4:8),"corrected y1 = ")

diff --git a/964/CH26/EX26.6/26_6.sce b/964/CH26/EX26.6/26_6.sce
new file mode 100755
index 000000000..b09fcb8ec
--- /dev/null
+++ b/964/CH26/EX26.6/26_6.sce
@@ -0,0 +1,19 @@
+//clc()

+disp("f(x,y) = 4*exp(0.8*x) - 0.5*y")

+//f'(x,y) = 4*exp(0.8*x) - 0.5*y

+h = 1;

+x = -3:h:4;

+y(1) = -4.547302;

+y(2) = -2.306160;

+y(3) = -0.3929953;

+y(4) = 2;

+m(4) = y(4);

+for i =4:7

+    y(i+1) = y(i) + h *(55* (4*exp(0.8*x(i)) - 0.5*y(i)) / 24 - 59 * (4*exp(0.8*x(i-1)) - 0.5*y(i-1)) / 24 + 37*(4*exp(0.8*x(i-2)) - 0.5*y(i-2))/24 - 9*(4*exp(0.8*x(i-3)) - 0.5*y(i-3))/24);

+    m(i+1) = y(i+1)

+    y(i+1) = y(i) + h*(9*(4*exp(0.8*x(i+1)) - 0.5*y(i+1))/24 +19*(4*exp(0.8*x(i)) - 0.5*y(i))/24 - 5*(4*exp(0.8*x(i-1)) - 0.5*y(i-1))/24 + (4*exp(0.8*x(i-2)) - 0.5*y(i-2))/24);

+end

+disp(x(4:8),"x = ")

+disp(m(4:8),"y0 = ")

+disp(y(4:8),"y1 = ")

+

diff --git a/964/CH26/EX26.7/26_7.sce b/964/CH26/EX26.7/26_7.sce
new file mode 100755
index 000000000..96fb04aed
--- /dev/null
+++ b/964/CH26/EX26.7/26_7.sce
@@ -0,0 +1,25 @@
+//clc()

+//dy/dx = -y

+//y = exp(-x)

+h = 0.5;

+x = -1.5:h:10;

+y(1) = exp(-x(1));

+y(2) = exp(-x(2));

+y(3) = exp(-x(3));

+y(4) = 1;

+m(4) = y(4);

+for  i = 4:23;

+    y(i+1) = y(i-3) + 4*h*(2*(-y(i)) + y(i-1) + 2*(-y(i-2)))/3;

+    m(i+1) = y(i+1);

+    y(i+1) = y(i-1) + h*(-y(i-1) +4 * (-y(i)) + (-y(i+1)))/3;

+end

+disp(x(4:24),"x = ")

+disp(m(4:24),"y0(milnes method) = ")

+disp(y(4:24),"corrected y1(milnes method) = ")

+for i =4:23

+    y(i+1) = y(i) + h *(55* (-y(i)) / 24 - 59 * (-y(i-1)) / 24 + 37*(-y(i-2))/24 - 9*(-y(i-3))/24);

+    m(i+1) = y(i+1)

+    y(i+1) = y(i) + h*(9*(-y(i+1))/24 +19*(-y(i))/24 - 5*(-y(i-1))/24 + (-y(i-2))/24);

+end

+disp(m(4:23),"y0(fourth order adams method) = ")

+disp(y(4:23),"y1(fourth order adams method) = ")