In this talk I will mainly focus on the existence and uniqueness of weak solutions to the nonlinear continuous coagulation and multiple fragmentation equations. In addition, the convergence analysis of two numerical methods (the fixed pivot technique and the cell average technique) for solving nonlinear coagulation or Smoluchowski equation is introduced. At the end, the convergence rates obtained from both the techniques are compared and mathematical results of the convergence analysis are also demonstrated numerically.