In the present paper, we describe Numerical solution of mathematical problems by strategically studying and researching the existing B-spline techniques. Here, we discussed the recursive relation for B-splines formulation by studying of B-splines of various degrees using different approaches. A comparative analysis between the resultant cubic spline applied on test equation with the existing cubic spline along with remarks is made in present study. A tabulated analysis of results of the present study is notable and at par with cubic spline.