1 files changed, 61 insertions, 0 deletions
diff --git a/260/CH13/EX13.18/13_18.sce b/260/CH13/EX13.18/13_18.sce
new file mode 100644
index 000000000..096181d62
--- /dev/null
+++ b/260/CH13/EX13.18/13_18.sce
@@ -0,0 +1,61 @@
+//Eg-13.18
+//pg-565
+
+clear
+clc
+
+deff('out = func(in1,in2)','out = (1-in2*sin(in1)/cos(in1))')
+
+x(1) = 0;
+y(1) = 0;
+
+h = 0.1;
+
+for(i = 1:10)
+    x(i+1) = x(i) + h;
+    
+end
+
+//Using RK method
+
+a = (2^0.5-1)/2;
+b = (2-2^0.5)/2;
+c = -(2^0.5)/2;
+d = 1 + (2^0.5)/2;
+
+printf('   x          y\n')
+
+for(i = 1:4)
+    
+    k1(i) = h*func(x(i),y(i));
+    k2(i) = h*func(x(i)+h/2,y(i)+k1(i)/2);
+    k3(i) = h*func(x(i)+h/2,y(i)+a*k1(i)+b*k2(i));
+    k4(i) = h*func(x(i)+h,y(i)+c*k2(i)+d*k3(i));
+    y(i+1) = y(i) + 1/6*(k1(i)+2*b*k2(i)+2*d*k3(i)+k4(i));
+    
+    
+end
+
+for(i = 2:4)
+    printf('%f    %f\n',x(i),y(i))
+end
+
+x4 = x(5);
+x3 = x(4);
+x2 = x(3);
+x1 = x(2);
+x0 = x(1);
+y3 = y(4);
+y2 = y(3);
+y1 = y(2);
+y0 = y(1);
+
+//Using the equation : y4 = 1/25*[48*y3 - 36*y2 + 16*y1 - 3*y0 + 12*h*func(x4,y4)]
+// => y4 - 1/25*12*h*func(x4,y4) = 1/25*[48*y3 - 36*y2 + 16*y1 - 3*y0 ]
+// => y4 = 0.39731/1.02029    analytically
+
+y4 = 0.39731/1.02029;
+
+printf('\n\nThe value of y4 = %f\n',y4)
+
+printf('\nThe analytical solution of this problem is y = sinx.\nThus, the exact solution is y(x = 0.4) = %f\n',y4)
+\ No newline at end of file