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

---
 1332/CH5/EX5.32/5_32.sce | 130 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 130 insertions(+)
 create mode 100755 1332/CH5/EX5.32/5_32.sce

(limited to '1332/CH5/EX5.32/5_32.sce')

diff --git a/1332/CH5/EX5.32/5_32.sce b/1332/CH5/EX5.32/5_32.sce
new file mode 100755
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--- /dev/null
+++ b/1332/CH5/EX5.32/5_32.sce
@@ -0,0 +1,130 @@
+//Example 5.32
+//Regula Falsi, Newton Raphson and Mullers Method
+//Page no. 201
+clc;clear;close;
+deff('x=f(x)','x=x^5-3.7*x^4+7.4*x^3-10.8*x^2+10.8*x-6.8')
+deff('x=f1(x)','x=5*x^4-4*3.7*x^3+3*7.4*x^2-21.6*x+10.8')
+//newton raphson
+printf('n\txn\t\t\f(xn)\t\tf1(xn)\t\tXn+1\t\tError\n')
+printf('-----------------------------------------------------------------------------------------------------\n')
+x0=1.5;e=0.00001
+for i=1:4
+    x1=x0-f(x0)/f1(x0)
+    e1=abs(x0-x1)
+    printf(' %i\t%.10f\t%.10f\t%.10f\t%.10f\t%.10f\n',i-1,x0,f(x0),f1(x0),x1,e1)
+    x0=x1;
+    if abs(x0)<e then
+        break;
+    end
+end
+printf('\n\nThe solution of this equation by newton raphshon after %i Iterations is %.10f\n\n\n',i,x1)
+
+//regula falsi
+x1=1;x2=2;e=0.00001
+printf('n\tx1\t\tf(x1)\t\tx2\t\tf(x2)\t\tx3\t\tf(x3)')
+printf('\n-------------------------------------------------------------------------------------------------\n')
+for i=0:7
+    x3=x2*f(x1)/(f(x1)-f(x2))+x1*f(x2)/(f(x2)-f(x1))
+    printf(' %i\t%f\t%f\t%f\t%f\t%f\t%f\n',i,x1,f(x1),x2,f(x2),x3,f(x3))
+    if f(x1)*f(x3)>0 then
+        x1=x3
+    else
+        x2=x3
+    end
+    if abs(f(x3))<e then
+        break
+    end
+end
+printf('\n\nTherefore the solution by regula falsi method after %i iterations is %.10g',i,x3)
+
+//mullers method
+zi=[1;2;3];
+s=["i","z0","z1","z2","f0","f1","f2","li","di","gi","li+1","hi","hi+1","zi+1","D+","D_"]
+li(1)=(zi(3,1)-zi(2,1))/(zi(2,1)-zi(1,1))
+hi(1)=zi(3,1)-zi(2,1);
+for i=2:6
+    for j=1:3
+       fz(j,i-1)=f(zi(j,i-1))
+    end
+    di(i-1)=1+li(i-1)
+    gi(i-1)=fz(1,i-1)*li(i-1)^2-fz(2,i-1)*di(i-1)^2+fz(3,i-1)*(li(i-1)+di(i-1))
+    D1(i-1)=gi(i-1)+sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))
+    D2(i-1)=gi(i-1)-sqrt(gi(i-1)^2-4*fz(3,i-1)*di(i-1)*li(i-1)*(fz(1,i-1)*li(i-1)-fz(2,i-1)*di(i-1)+fz(3,i-1)))
+    if abs(D1(i-1))>abs(D2(i-1)) then
+        li(i)=-2*fz(3,i-1)*di(i-1)/D1(i-1)
+    else
+        li(i)=-2*fz(3,i-1)*di(i-1)/D2(i-1)
+    end
+    hi(i)=li(i)*hi(i-1);
+    z(i-1)=zi(3,i-1)+hi(i)
+    for j=1:2
+        zi(j,i)=zi(j+1,i-1)
+    end
+    zi(3,i)=z(i-1)
+end
+printf('\n\n ')
+for i=1:16
+    if i==1 then
+        printf(s(i))
+        for j=1:5
+            printf('\t\t\t %i',j-1)
+        end
+        printf('\n----------------------------------------------------------------------------------------------------------------------------------')
+    elseif i<=4
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',zi(i-1,j))
+        end
+    elseif i<=7
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',fz(i-4,j))
+        end
+    elseif i<=8
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',li(j))
+        end
+    elseif i<=9
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',di(j))
+        end
+    elseif i<=10
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',gi(j))
+        end
+    elseif i<=11
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',li(j+1))
+        end
+    elseif i<=12
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',hi(j))
+        end
+        elseif i<=13
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',hi(j+1))
+        end
+        elseif i<=14
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',z(j))
+        end
+        elseif i<=15
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',D1(j))
+        end
+        elseif i<=16
+        printf('\n %s',s(i))
+        for j=1:5
+            printf('\t\t%.10f',D2(j))
+        end
+    end
+end
+printf('\n\nAt the end of the %ith iteration by mullers method, the root of the equation is %.10f',j-1,z(j))
\ No newline at end of file
-- 
cgit