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+// example 7.4
+// solve by shooting method;
+
+//   u''=2*u*u';
+// u(0)=0.5;  u(1)=1;              
+
+// let ->   U1(x)=du/dx;
+// U2(x)=d2u/dx2;
+
+// U(x)=[U1(x);U2(x)]
+
+// hence ;
+// dU/dx=f(x,U);
+
+h=.25;
+
+ub=[.5,1];
+
+up=[0:.1:1];
+ 
+x=0:h:1;
+ 
+deff('[w]=f(x,U)','w=[U(2); 2*U(1)*U(2)]')
+
+
+[U] = shooting(ub,up,x,f);
+
+// the solution obtained would show the values of u in the first collumn and their corresponding  derivatives in the second collumn ;
+\ No newline at end of file