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

---
 50/CH5/EX5.17/ex_5_17.sce | 24 ++++++++++++++++++++++++
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 create mode 100755 50/CH5/EX5.17/ex_5_17.sce

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diff --git a/50/CH5/EX5.17/ex_5_17.sce b/50/CH5/EX5.17/ex_5_17.sce
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+// example 5.17
+// caption: gauss-legendre method
+// I= integral 2*x/(1+x^4) in the range [1,2];
+// first we need ti transform the interval [1,2 ] to [-1,1], since gauss-legendre three point method is applicable in the range[-1,1],
+
+// let t=ax+b;
+// solving for a,b from the two ranges, we get a=1/2; b=3/2; x=(t+3)/2;
+
+// hence I=integral  2*x/(1+x^4) in the range [0,1]= integral 8*(t+3)/16+(t+3)^4 in the range [-1,1];
+
+
+deff('[y]=f(t)','y=8*(t+3)/(16+(t+3)^4) ');
+
+// 1) since , from gauss legendre one point rule;
+I1=2*f(0)
+
+// 2) since , from gauss legendre two point rule;
+I2=f(-1/sqrt(3))+f(1/sqrt(3))
+
+// 3) since , from gauss legendre three point rule;
+I=(1/9)*(5*f(-sqrt(3/5))+8*f(0)+5*f(sqrt(3/5))) 
+
+
+// we know , exact solution is 0.5404;
\ No newline at end of file
-- 
cgit