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authorpriyanka2015-06-24 15:03:17 +0530
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+//Example 15.24
+//Improved Milne Simpson Predictor Corrector Method
+//Page no. 546
+clc;clear;close;
+
+deff('y=f(x,y)','y=y-x^2')
+y(1)=1;h=0.25;x=0;
+printf('n\tXn\tYn\tfn\tY`n\tYn\tY`n+1\tm(n+1)\tv(n+1)\n------------------------------------------------------------------------\n')
+f1(1)=f(x,y(1));
+for i=1:3
+ K1=h*f(x,y(i));
+ K2=h*f(x+2*h/3,y(i)+2*K1/3);
+ y(i+1)=y(i)+(K1+3*K2)/4
+ printf(' %i\t%.3f\t%.3f\t%.3f\n',i-1,x,y(i),f1(i))
+ x=x+h
+ f1(i+1)=f(x,y(i+1))
+end
+Y31=0
+for i=3:10
+ Y41=y(i-2)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3 //predictor
+ m4=Y41+28*(y(i+1)-Y31)/29 //modifier
+ v4=f(x+h,m4) //evaluator
+ Y4=y(i)+h*(v4+4*f1(4)+f1(3))/3 //corrector
+ printf(' %i\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\t%.3f\n',i,x,y(i+1),f1(4),Y31,y(i+1),Y41,m4,v4)
+ y(i+2)=Y4
+ Y31=Y41;
+ f1(2)=f1(3);
+ f1(3)=f1(4);
+ f1(4)=f(x+h,y(i+2))
+ x=x+h
+end