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+                                   // The equation cos(x)-x*%e^x==0 has  real roots.
+                                   // the graph of this function can be observed here.
+xset('window',25);                                   
+x=0:.01:2;                                             // defining the range of x.
+deff('[y]=f(x)','y=cos(x)-x*%e^x');                  //defining the cunction.
+y=feval(x,f);
+ 
+a=gca(); 
+ 
+a.y_location = "origin";
+ 
+a.x_location = "origin"; 
+plot(x,y)                                                  // instruction to plot the graph 
+title(' y = cos(x)-x*%e^x')
+
+// from the above plot we can infre that the function has root between   
+// the interval (0,1)
+
+x0=0;
+
+         //solution using linear iteration method for the first two iterations and aitken's process two times for the third iteration.
+         
+         deff('[y]=g(x)','y=x+1/2*(cos(x)-x*%e^x)');
+         deff('[y]=gp(x)','y=1+1/2*(-sin(x)-x*%e^x-%e^x)');
+         
+         
+generaliteration2(x0,g,gp)
+
+
+// from the above iterations performed we can infer that-
+x1=0.50000000;
+x2=0.5266110;
+
+
+
+aitken(x0,x1,x2,g)          // calling the aitken method for one iteration