Homotopy analysis method for Burgers’ equation: Application of gradient descent approach

The present work provide a synthesis towards understanding the advantage of the gradient descent method applied over the homotopy analysis method (HAM). To demonstrate the idea, the nonlinear Burgers’, equation is taken into consideration. Due to the possibility of strong nonlinearity, most of the PDEs are solved by using either numerical or approximate analytical techniques. The HAM is one of the approximate analytical technique consist of auxiliary parameter h which allows us to adjust and control the convergence region of the series solution. The chosen value of h from the convergence region may possibility to produce diverging solution due to trial and error approach. Hence, the convergence to correct solution and its accuracy need to be ascertained. Therefore, the development of efficient iterative optimization approach namely gradient descent method may establish the correct values of h and gives the precise solution. In order to establish efficacy of proposed method, the Burgers’ equation results obtained from gradient descent approach are validated with existing analytical and numerical results reported in the literature. The novelty of proposed work would in a way to demonstrate the potential and effectiveness of gradient descent method for evaluating the various kinds of nonlinear equation.