Problems on Numerical Technique - II:

Example-1 find from the following table, the area bounded by the curve and x-axis from x = 7.47 to x = 7.52

           

Solution: We know that the required area under curve would be

            

With h = 0.01, The Trepezodial Rule

    

gives;

          

Example-2 Use Picard’s method to approximate the value of y at x = 0.1 given that

Solution: Given dy/dx = y−x/y x Hence Picard’s Iteration equation is

          

which gives First approximation

      

Second approximation;

       

which is quite difficult to integrate. So we stop our process here. We use only first order approximation. By putting x = 0.1