From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 964/CH25/EX25.1/25_1.sce      |  20 +++++++++++++++
 964/CH25/EX25.10/25_10.sce    |  30 ++++++++++++++++++++++
 964/CH25/EX25.11/25_11.sce    |  57 ++++++++++++++++++++++++++++++++++++++++++
 964/CH25/EX25.11/25_11_1.jpeg | Bin 0 -> 49514 bytes
 964/CH25/EX25.11/25_11_2.jpeg | Bin 0 -> 64555 bytes
 964/CH25/EX25.12/25_12.sce    |  39 +++++++++++++++++++++++++++++
 964/CH25/EX25.13/25_13.sce    |  27 ++++++++++++++++++++
 964/CH25/EX25.14/25_14.jpeg   | Bin 0 -> 26345 bytes
 964/CH25/EX25.14/25_14.sce    |  10 ++++++++
 964/CH25/EX25.2/25_2.sce      |  11 ++++++++
 964/CH25/EX25.3/25_3.sce      |  20 +++++++++++++++
 964/CH25/EX25.4/25_4.jpeg     | Bin 0 -> 31646 bytes
 964/CH25/EX25.4/25_4.sce      |  24 ++++++++++++++++++
 964/CH25/EX25.5/25_5.sce      |  21 ++++++++++++++++
 964/CH25/EX25.6/25_6.sce      |  28 +++++++++++++++++++++
 964/CH25/EX25.7/25_7.sce      |  33 ++++++++++++++++++++++++
 964/CH25/EX25.8/25_8.sce      |  57 ++++++++++++++++++++++++++++++++++++++++++
 964/CH25/EX25.9/25_9.sce      |  15 +++++++++++
 18 files changed, 392 insertions(+)
 create mode 100755 964/CH25/EX25.1/25_1.sce
 create mode 100755 964/CH25/EX25.10/25_10.sce
 create mode 100755 964/CH25/EX25.11/25_11.sce
 create mode 100755 964/CH25/EX25.11/25_11_1.jpeg
 create mode 100755 964/CH25/EX25.11/25_11_2.jpeg
 create mode 100755 964/CH25/EX25.12/25_12.sce
 create mode 100755 964/CH25/EX25.13/25_13.sce
 create mode 100755 964/CH25/EX25.14/25_14.jpeg
 create mode 100755 964/CH25/EX25.14/25_14.sce
 create mode 100755 964/CH25/EX25.2/25_2.sce
 create mode 100755 964/CH25/EX25.3/25_3.sce
 create mode 100755 964/CH25/EX25.4/25_4.jpeg
 create mode 100755 964/CH25/EX25.4/25_4.sce
 create mode 100755 964/CH25/EX25.5/25_5.sce
 create mode 100755 964/CH25/EX25.6/25_6.sce
 create mode 100755 964/CH25/EX25.7/25_7.sce
 create mode 100755 964/CH25/EX25.8/25_8.sce
 create mode 100755 964/CH25/EX25.9/25_9.sce

(limited to '964/CH25')

diff --git a/964/CH25/EX25.1/25_1.sce b/964/CH25/EX25.1/25_1.sce
new file mode 100755
index 000000000..3b6647efd
--- /dev/null
+++ b/964/CH25/EX25.1/25_1.sce
@@ -0,0 +1,20 @@
+//clc()
+//dy/dx = -2*x^3 + 12*x^2 - 20*x + 8.5
+//therefore, y = -0.5*x^4 + 4*x^3 - 10*x^2 + 8.5 + c
+x1 = 0;
+y1 = 1;
+h = 0.5;
+c =-(-0.5*x1^4 + 4*x1^3 - 10*x1^2 + 8.5*x1 - y1);
+x = 0:0.5:4;
+disp(x,"x = ")
+y = -0.5*x^4 + 4*x^3 - 10*x^2 + 8.5*x + c;
+disp(y,"true values of y = ")
+fxy = -2*x^3 + 12*x^2 - 20*x + 8.5;
+y2(1) = y(1);
+e(1) = (y(1) - y2(1)) * 100 / y(1);
+for i = 2:9
+    y2(i) = y2(i-1) + fxy(i-1)*h;
+    e(i) = (y(i) - y2(i))*100/y(i);
+end
+disp(y2,"y by euler method =")
+disp(e,"error =")
diff --git a/964/CH25/EX25.10/25_10.sce b/964/CH25/EX25.10/25_10.sce
new file mode 100755
index 000000000..95feeae4c
--- /dev/null
+++ b/964/CH25/EX25.10/25_10.sce
@@ -0,0 +1,30 @@
+//clc()
+//dy1/dx = -0.5*y1
+//dy2/dx = 4 - 0.3*y2 - 0.1*y1
+x1 = 0;
+h =0.5;
+y1(1) = 4;
+y2(1) = 6;
+x = 0:h:2;
+for i = 1:5
+    k11(i) = -0.5*y1(i);
+    k12(i) = 4 - 0.3*y2(i) - 0.1*y1(i);
+    y11 = y1(i) + k11(i) * h/2;
+    y21 = y2(i) + k12(i) * h/2;
+    k21(i) = -0.5*y11;
+    k22(i) = 4 - 0.3*y21 - 0.1*y11;
+    y11 = y1(i) + k21(i) * h/2;
+    y21 = y2(i) + k22(i) * h/2;
+    k31(i) = -0.5*y11;
+    k32(i) = 4 - 0.3*y21 - 0.1*y11;
+    y11 = y1(i) + k31(i) * h;
+    y21 = y2(i) + k32(i) * h;
+    k41(i) = -0.5*y11;
+    k42(i) = 4 - 0.3*y21 - 0.1*y11;
+    y1(i+1) = y1(i) + ( k11(i) + 2*k21(i) + 2*k31(i) + k41(i) )*h / 6;
+    y2(i+1) = y2(i) + ( k12(i) + 2*k22(i) + 2*k32(i) + k42(i) ) *h/ 6;
+end
+disp("using fourth order RK method")
+disp(x,"x =")
+disp(y1(1:5),"y1 = ")
+disp(y2(1:5),"y2 = ")
diff --git a/964/CH25/EX25.11/25_11.sce b/964/CH25/EX25.11/25_11.sce
new file mode 100755
index 000000000..ec5a7c7c2
--- /dev/null
+++ b/964/CH25/EX25.11/25_11.sce
@@ -0,0 +1,57 @@
+clc;
+clear;
+function yp=f(x,y)
+    yp=[y(2);-16.1*y(1)];
+endfunction
+x=0:0.1:4
+y0=[0.1 0];
+sol=ode(y0,0,x,f);
+count=1;
+disp(sol)
+for i=1:2:81
+    a(count)=sol(i);
+    b(count)=sol(i+1);
+    count=count+1;
+end
+plot(x,a)
+plot(x,b,".-")
+h1=legend(["y1,y3","y2,y4"])
+xtitle("y vs x","x","y")
+function yp=g(x,y)
+    yp=[y(2);-16.1*sin(y(1))];
+endfunction
+sol=ode(y0,0,x,g);
+count=1;
+disp(sol)
+for i=1:2:81
+    a(count)=sol(i);
+    b(count)=sol(i+1);
+    count=count+1;
+end
+plot(x,a)
+plot(x,b,".-")
+clf();
+y0=[%pi/4 0];
+sol=ode(y0,0,x,f);
+count=1;
+disp(sol)
+for i=1:2:81
+    a(count)=sol(i);
+    b(count)=sol(i+1);
+    count=count+1;
+end
+plot(x,a)
+plot(x,b,".-")
+
+xtitle("y vs x","x","y")
+sol=ode(y0,0,x,g);
+count=1;
+disp(sol)
+for i=1:2:81
+    a(count)=sol(i);
+    b(count)=sol(i+1);
+    count=count+1;
+end
+plot(x,a,'o-')
+plot(x,b,"x-")
+h1=legend(["y1","y2","y3","y4"])
diff --git a/964/CH25/EX25.11/25_11_1.jpeg b/964/CH25/EX25.11/25_11_1.jpeg
new file mode 100755
index 000000000..b8f1e82d5
Binary files /dev/null and b/964/CH25/EX25.11/25_11_1.jpeg differ
diff --git a/964/CH25/EX25.11/25_11_2.jpeg b/964/CH25/EX25.11/25_11_2.jpeg
new file mode 100755
index 000000000..952c87781
Binary files /dev/null and b/964/CH25/EX25.11/25_11_2.jpeg differ
diff --git a/964/CH25/EX25.12/25_12.sce b/964/CH25/EX25.12/25_12.sce
new file mode 100755
index 000000000..ae67f03a0
--- /dev/null
+++ b/964/CH25/EX25.12/25_12.sce
@@ -0,0 +1,39 @@
+//clc()
+disp("f(x,y) = 4*exp(0.8*x) - 0.5*y")
+//f'(x,y) = 4*exp(0.8*x) - 0.5*y
+x = 0:2:2;
+y(1) = 2;
+h =2;
+t = 14.84392;
+k1 = 4*exp(0.8*x(1)) - 0.5*y(1);
+x1 = x(1) + h/2;
+y1 = y(1) + k1*h/2;
+k2 = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(1) + h/2;
+y1 = y(1) + k2*h/2;
+k3 = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(1) + h;
+y1 = y(1) + k3*h;
+k4 = 4*exp(0.8*x1) - 0.5*y1;
+y(2) = y(1) + (k1 + 2*k2 + 2*k3 + k4)*h/6;
+e = (t - y(2))/(t);
+disp(y(1:2),"y by h = 2 is")
+disp(e,"error = ")
+h = 1;
+x = 0:h:2;
+for i=1:3
+    k1(i) = 4*exp(0.8*x(i)) - 0.5*y(i);
+    x1 = x(i) + h/2;
+    y1 = y(i) + k1(i)*h/2;
+    k2(i) = 4*exp(0.8*x1) - 0.5*y1;
+    x1 = x(i) + h/2;
+    y1 = y(i) + k2(i)*h/2;
+    k3(i) = 4*exp(0.8*x1) - 0.5*y1;
+    x1 = x(i) + h;
+    y1 = y(i) + k3(i)*h;
+    k4(i) = 4*exp(0.8*x1) - 0.5*y1;
+    y(i+1) = y(i) + (k1(i) + 2*k2(i) + 2*k3(i) + k4(i))*h/6;    
+end
+e = (t - (y(3)))/t;
+disp(y(1:3),"y by h = 1 is")
+disp(e,"error = ")
diff --git a/964/CH25/EX25.13/25_13.sce b/964/CH25/EX25.13/25_13.sce
new file mode 100755
index 000000000..a0c5ba8ae
--- /dev/null
+++ b/964/CH25/EX25.13/25_13.sce
@@ -0,0 +1,27 @@
+//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 =2;
+x = 0:h:2;
+y(1) = 2;
+t = 14.84392;
+k1 = 4*exp(0.8*x(1)) - 0.5*y(1);
+x1 = x(1) + h/5;
+y1 = y(1) + k1*h/5;
+k2 = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(1) + 3*h/10;
+y1 = y(1) + 3*k1*h/40 + 9*k2*h/40;
+k3 = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(1) + 3*h/5;
+y1 = y(1) + 3*k1*h/10 - 9*k2*h/10 + 6*k3*h/5;
+k4 = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(1) + h;
+y1 = y(1) -11*k1*h/54 + 5*k2*h/2 - 70*k3*h/27 + 35*k4*h/27;
+k5 = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(1) + 7*h/8;
+y1 = y(1) + 1631*k1*h/55296 + 175*k2*h/512 + 575*k3*h/13824 + 44275*k4*h/110592 +253*k5*h/4096;
+k6 = 4*exp(0.8*x1) - 0.5*y1;
+y1 = y(1) + (37*k1/378 + 250*k3/621 + 125*k4/594 + 512*k6/1771)*h;
+y2 = y(1) + (2825*k1/27648 + 18575*k3/48384 + 13525*k4/55296 + 277*k5/14336 + k6/4)*h;
+disp(y1,"y ( fourth order prediction ) = ")
+disp(y2,"y ( fifth order prediction ) = ")
diff --git a/964/CH25/EX25.14/25_14.jpeg b/964/CH25/EX25.14/25_14.jpeg
new file mode 100755
index 000000000..73b0a44b9
Binary files /dev/null and b/964/CH25/EX25.14/25_14.jpeg differ
diff --git a/964/CH25/EX25.14/25_14.sce b/964/CH25/EX25.14/25_14.sce
new file mode 100755
index 000000000..66b236d37
--- /dev/null
+++ b/964/CH25/EX25.14/25_14.sce
@@ -0,0 +1,10 @@
+clc;
+clear;
+function yp=f(x,y)
+    yp=10*exp(-(x-2)^2/(2*(0.075^2)))-0.6*y
+endfunction
+x=0:0.1:4
+y0=0.5;
+sol=ode(y0,0,x,f);
+plot(x,sol)
+xtitle("y vs x","x","y")
diff --git a/964/CH25/EX25.2/25_2.sce b/964/CH25/EX25.2/25_2.sce
new file mode 100755
index 000000000..02feb97b4
--- /dev/null
+++ b/964/CH25/EX25.2/25_2.sce
@@ -0,0 +1,11 @@
+//clc()
+//f(x,y) = dy/dx = -2*x^3 + 12*x^2 - 20*x + 8.5
+//f'(x,y) = -6*x^2 + 24*x - 20
+//f"(x,y) = -12*x + 24
+//f"'(x,y) = -12
+x = 0;
+Et2 = (-6*x^2 + 24*x - 20) * 0.5^2 / 2;
+Et3 = (-12*x + 24) * (0.5)^3 / 6;
+Et4 = (-12) *(0.5 ^ 4) / 24;
+Et = Et2 + Et3 + Et4;
+disp(Et,"Total truncation error =")
diff --git a/964/CH25/EX25.3/25_3.sce b/964/CH25/EX25.3/25_3.sce
new file mode 100755
index 000000000..7cf519d87
--- /dev/null
+++ b/964/CH25/EX25.3/25_3.sce
@@ -0,0 +1,20 @@
+//clc()
+//dy/dx = -2*x^3 + 12*x^2 - 20*x + 8.5
+//therefore, y = -0.5*x^4 + 4*x^3 - 10*x^2 + 8.5 + c
+x1 = 0;
+y1 = 1;
+h = 0.25;
+c =-(-0.5*x1^4 + 4*x1^3 - 10*x1^2 + 8.5*x1 - y1);
+x = 0:h:4;
+disp(x,"x = ")
+y = -0.5*x^4 + 4*x^3 - 10*x^2 + 8.5*x + c;
+disp(y,"true values of y = ")
+fxy = -2*x^3 + 12*x^2 - 20*x + 8.5;
+y2(1) = y(1);
+e(1) = (y(1) - y2(1)) * 100 / y(1);
+for i = 2:17
+    y2(i) = y2(i-1) + fxy(i-1)*h;
+    e(i) = (y(i) - y2(i))*100/y(i);
+end
+disp(y2,"y by euler method =")
+disp(e,"error =")
diff --git a/964/CH25/EX25.4/25_4.jpeg b/964/CH25/EX25.4/25_4.jpeg
new file mode 100755
index 000000000..88a957dfb
Binary files /dev/null and b/964/CH25/EX25.4/25_4.jpeg differ
diff --git a/964/CH25/EX25.4/25_4.sce b/964/CH25/EX25.4/25_4.sce
new file mode 100755
index 000000000..e2ef29404
--- /dev/null
+++ b/964/CH25/EX25.4/25_4.sce
@@ -0,0 +1,24 @@
+clc;
+clear;
+m=68.1;
+g=9.8;
+c=12.5;
+a=8.3;
+b=2.2;
+vmax=46;
+function yp=f(t,v)
+    yp=g-c*v/m;
+endfunction
+v0=0;
+t=0:15;
+x=ode(v0,0,t,f);
+disp(x)
+plot(t,x,'.-')
+
+function yp=f1(t,v)
+    yp=g-(c/m)*(v+a*(v/vmax)^b)
+endfunction
+x1=ode(v0,0,t,f1);
+plot(t,x1)
+xtitle("velocity vs time","t (s)","v (m/s)")
+h1=legend(["Linear";"Nonlinear"])
diff --git a/964/CH25/EX25.5/25_5.sce b/964/CH25/EX25.5/25_5.sce
new file mode 100755
index 000000000..111e8d0ca
--- /dev/null
+++ b/964/CH25/EX25.5/25_5.sce
@@ -0,0 +1,21 @@
+//clc()
+//y' = 4*exp(0.8*x) - 0.5*y
+//y = 4*(exp(0.8*x) - exp(-0.5*x))/1.3 + 2*exp(-0.5*x)
+x = 0:1:4;
+disp(x)
+x1 = 0;
+y1 = 2;
+y2(1) = y1;
+for i = 1:5
+    y(i) = 4*(exp(0.8*x(i)) - exp(-0.5*x(i)))/1.3 + 2*exp(-0.5*x(i));
+    dy(i) = 4*exp(0.8*x(i)) - 0.5*y2(i);
+    y2(i + 1) = y2(i) + dy(i);
+    if i>1 then
+        m(i) = (dy(i) + dy(i-1))/2;
+        y2(i) = y2(i-1) + m(i);
+        dy(i) = 4*exp(0.8*x(i)) - 0.5*y2(i);
+    end
+    e(i) = (y(i) - y2(i)) * 100 / y(i);
+end
+disp(y2(1:5),"By heuns method(1 iteration)")
+disp("%",e(1:5),"error = ")
diff --git a/964/CH25/EX25.6/25_6.sce b/964/CH25/EX25.6/25_6.sce
new file mode 100755
index 000000000..9bc14bc87
--- /dev/null
+++ b/964/CH25/EX25.6/25_6.sce
@@ -0,0 +1,28 @@
+//clc()
+//f'(x,y) = -2*x^3 + 12*x^2 -20*x + 8.5
+//f(x,y) = -x^4 / 2 + 4*x^3 - 10*x^2 + 8.5*x + 1
+h = 0.5;
+x = 0:h:4;
+y1 = -x^4 / 2 + 4*x^3 - 10*x^2 + 8.5*x + 1;
+y(1) = 1;
+disp(x,"x =")
+disp(y1,"true value of y =")
+for i = 1:8
+    k1(i) = -2*x(i)^3 + 12*x(i)^2 -20*x(i) + 8.5;
+    x1(i) = x(i) + h/2;
+    k2(i) = -2*x1(i)^3 + 12*x1(i)^2 -20*x1(i) + 8.5;
+    y(i+1) = y(i) + k2(i)*h;
+    e(i) = (y1(i) - y(i))*100/y1(i);
+end
+disp(y(1:9),"y by midpoint method")
+disp(e,"error = ")
+for i = 1:8
+    k1(i) = -2*x(i)^3 + 12*x(i)^2 -20*x(i) + 8.5;
+    x(i) = x(i) + 3*h/4;
+    k2(i) = -2*x(i)^3 + 12*x(i)^2 -20*x(i) + 8.5;
+    y(i+1) = y(i) + (k1(i)/3 + 2*k2(i)/3)*h;
+    e(i) = (y1(i) - y(i))*100/y1(i);
+end
+disp(y(1:9),"y by second order Ralston RK")
+disp(e,"error = ")
+
diff --git a/964/CH25/EX25.7/25_7.sce b/964/CH25/EX25.7/25_7.sce
new file mode 100755
index 000000000..ce01ffb75
--- /dev/null
+++ b/964/CH25/EX25.7/25_7.sce
@@ -0,0 +1,33 @@
+//clc()
+//f'(x,y) = -2*x^3 + 12*x^2 -20*x + 8.5
+//f(x,y) = -x^4 / 2 + 4*x^3 - 10*x^2 + 8.5*x + 1
+h = 0.5;
+x = 0:h:4;
+y1 = -x^4 / 2 + 4*x^3 - 10*x^2 + 8.5*x + 1;
+y(1) = 1;
+for i=1:8
+     k1(i) = -2*x(i)^3 + 12*x(i)^2 -20*x(i) + 8.5;
+    x1(i) = x(i) + h/2;
+    k2(i) = -2*x1(i)^3 + 12*x1(i)^2 -20*x1(i) + 8.5;
+    k3(i) = -2*x1(i)^3 + 12*x1(i)^2 -20*x1(i) + 8.5;
+    x2(i) = x(i) + h;
+    k4(i) = -2*x2(i)^3 + 12*x2(i)^2 -20*x2(i) + 8.5;
+    y(i+1) = y(i) + (k1(i)+2*k2(i)+2*k3(i)+k4(i))*h/6;
+    e(i) = (y1(i) - y(i))*100/y1(i);
+end
+disp("f(x,y) = -2*x^3 + 12*x^2 -20*x + 8.5")
+disp(y(1:9),"y by fourth order Ralston RK")
+disp("f(x,y) = 4*exp(0.8*x) - 0.5*y")
+x = 0:h:0.5;
+y(1) = 2;
+k1 = 4*(exp(0.8*x(1)))-0.5*y(1);
+x1 = x(1) + 0.5*h;
+y1 = y(1) + 0.5*k1*h;
+k2 = 4*exp(0.8*x1) - 0.5*y1;
+y2 = y(1) + 0.5*k2*h;
+k3 = 4*exp(0.8*x1) - 0.5*y2;
+x1 = x(1) + h;
+y1 = y(1) + k3*h;
+k4 = 4*exp(0.8*x1) - 0.5*y1;
+y(2) = y(1) + (k1+2*k2+2*k3+k4)*h/6;
+disp(y(1:2),"y = ")
diff --git a/964/CH25/EX25.8/25_8.sce b/964/CH25/EX25.8/25_8.sce
new file mode 100755
index 000000000..9ec20d157
--- /dev/null
+++ b/964/CH25/EX25.8/25_8.sce
@@ -0,0 +1,57 @@
+//clc()
+disp("f(x,y) = 4*exp(0.8*x) - 0.5*y")
+h = 1;
+x = 0:h:4;
+y(1) = 2;
+for i = 1:5
+    k1(i) = 4*(exp(0.8*x(i)))-0.5*y(i);
+    x1 = x(i) + h;
+    y1 = y(i) + k1(i)*h;
+    k2(i) = 4*(exp(0.8*x1))-0.5*y1;
+    y(i+1) = y(i) + (k1(i)/2 + k2(i)/2)*h;
+end
+disp(y(1:5),"y(second order RK method) = ")
+for i = 1:5
+    k1(i) = 4*(exp(0.8*x(i)))-0.5*y(i);
+    x1 = x(i) + 0.5*h;
+    y1 = y(i) + 0.5*h*k1(i);
+    k2(i) = 4*(exp(0.8*x1))-0.5*y1;
+    x1 = x(i) + h;
+    y1 = y(i) -k1(i)*h + 2*k2(i)*h;
+    k3(i) = 4*(exp(0.8*x1))-0.5*y1;
+    y(i+1) = y(i) + (k1(i) + 4*k2(i) + k3(i))*h/6;
+end
+disp(y(1:5),"y(third order RK method) = ")
+for i = 1:5
+k1(i) = 4*(exp(0.8*x(i)))-0.5*y(i);
+x1 = x(i) + 0.5*h;
+y1 = y(i) + 0.5*k1(i)*h;
+k2(i) = 4*exp(0.8*x1) - 0.5*y1;
+y2 = y(i) + 0.5*k2(i)*h;
+k3(i) = 4*exp(0.8*x1) - 0.5*y2;
+x1 = x(i) + h;
+y1 = y(i) + k3(i)*h;
+k4(i) = 4*exp(0.8*x1) - 0.5*y1;
+y(i+1) = y(i) + (k1(i)+2*k2(i)+2*k3(i)+k4(i))*h/6;
+end
+disp(y(1:5),"y(fourth order RK method) = ")
+for i = 1:5
+    
+k1(i) = 4*(exp(0.8*x(i)))-0.5*y(i);
+x1 = x(i) + 0.25*h;
+y1 = y(i) + 0.25*k1(i)*h;
+k2(i) = 4*exp(0.8*x1) - 0.5*y1;
+y2 = y(i) + 0.125*k2(i)*h + 0.125*k1(i)*h;
+k3(i) = 4*exp(0.8*x1) - 0.5*y2;
+x1 = x(i) + 0.5*h;
+y1 = y(i) -0.5*k2(i)*h + k3(i)*h;
+k4(i) = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(i) + 0.75*h;
+y1 = y(i) + 3*k1(i)*h/16 + 9*k4(i)*h/16;
+k5(i) = 4*exp(0.8*x1) - 0.5*y1;
+x1 = x(i) + h;
+y1 = y(i) - 3*k1(i)*h/7 + 2*k2(i)*h/7 + 12*k3(i)*h/7 - 12*k4(i)*h/7 + 8*k5(i)*h/7;
+k6(i) = 4*exp(0.8*x1) - 0.5*y1;
+y(i+1) = y(i) + (7*k1(i)+32*k3(i)+12*k4(i) + 32*k5(i) + 7*k6(i))*h/90;
+end
+disp(y(1:5),"y(fifth order RK method)")
diff --git a/964/CH25/EX25.9/25_9.sce b/964/CH25/EX25.9/25_9.sce
new file mode 100755
index 000000000..ba1c4f88b
--- /dev/null
+++ b/964/CH25/EX25.9/25_9.sce
@@ -0,0 +1,15 @@
+//clc()
+//dy1/dx = -0.5*y1
+//dy2/dx = 4 - 0.3*y2 - 0.1*y1
+x1 = 0;
+h =0.5;
+y1(1) = 4;
+y2(1) = 6;
+x = 0:h:2;
+for i = 2:5
+    y1(i) = y1(i-1)  -0.5*y1(i-1)*h;
+    y2(i) = y2(i-1) + (4 - 0.3*y2(i-1) - 0.1*y1(i-1))*h;
+end
+disp(x,"x = ")
+disp(y1,"y1 = ")
+disp(y2,"y2 = ")
-- 
cgit