An approximation to the solution of hyperbolic equation by homotopy analysis method - Ismail, Siti Hajar (2018)
In this research, Homotopy Analysis Method (HAM) is a analytical method that be used to obtained the approximation solution of hyperbolic equation. Hyperbolic equation is a one of the class of Partial Differential Equation (PDE). PDE is one of the basic areas of applied analysis, and it is difficult to imagine any area of applications where its impact is not felt. In recent decades, there has been tremendous emphasis on understanding and modelling nonlinear processes by using nonlinear PDE. Basically the nonlinear PDE is difficult to solve compare to linear PDE. So, HAM is introduced to solve hyperbolic equation for both linear and nonlinear equation. The auxiliary parameter ~ in the HAM solutions has provided a convenient way of controlling the convergence region of series solution. This method is reliable and manageable to get the approximation solution.The optimum approximation solution of nonlinear hyperbolic equation can be easier obtain by HAM due to it always provides a family of solution expressions in the auxiliary parameter and the convergence. It shown that in HAM even different numbers of auxiliary parameter, ~ is used, the approximation solution still converge to the exact solution.