• ### Reinitiated Laplace Homotopy Ananlysis Method For Solving Integral Equations

Kong Hoong Lem

Abstract: The complexity of the deformation equation increases exponentially with the order of approximation.  Consequently, implementing the Laplace homotopy analysis method (LHAM) under high deformation order can be very computationally costly and lengthy and even cause computational paralysis in cases. Here, the LHAM is modified in a reinitiated manner where the low order results are initiated for further approximation using truncated Maclaurin expansions. This modified approach manages to avoid high order approximation but still promises accurate approximate series solution. This approach greatly improves the efficiency of LHAM in solving integral equations.

Keywords: Laplace transform, homotopy analysis method (HAM), integral equations.