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//Example 15.25
//Hamming Predictor Corrector Method
//Page no. 548
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\tYc(n)\tY`n+1\tm(n+1)\tv(n+1)\tYc(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=y(4);Yc=0
for i=3:10
Y41=y(i-2)+4*h*(2*f1(4)-f1(3)+2*f1(2))/3 //predictor
m4=Y41+112*(Y31-Yc)/121 //modifier
v4=f(x+h,m4) //evaluator
Y4c=(9*y(i+1)-y(i-1))/8+3*h*(v4+2*f1(4)-f1(3))/8 //corrector
Y4=Y4c+9*(Y41-Y4c)/121 //final value
printf(' %i\t%.3f\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,Yc,Y41,m4,v4,Y4c)
y(i+2)=Y4
Y31=Y41;
f1(2)=f1(3);
f1(3)=f1(4);
f1(4)=f(x+h,y(i+2))
Yc=Y4c
x=x+h
end
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