Enhanced Laplace Adomian Decomposition Method for Nonlinear Volterra Integral Equation

Abstract

The Adomian Decomposition Method (ADM) can be directly applied with constant or variable coefficients without using linearization, destruction or some other unpreferable assumptions. The ADM is found rapidly converging on several type of ordinary and partial differential equations. Though, some valuable and significant modification in ADM like Laplace Adomian Decomposition Method (LADM) and Modified Laplace Adomian Decomposition Method (MLADM) were introduced by researchers. Despite better performance, the effectiveness, weaknesses and inconsistencies of traditional and modification in ADM need to be explored. Moreover, the performance and efficiency of Laplace based ADM need to be further improved. Accordingly, the strength of two existing modifications LADM and MLADM in ADM is integrated and a new technique named Enhanced Laplace Adomian Decomposition Method (ELADM) is introduced in this paper. Some illustrative examples are provided to analyze the working of proposed ELADM, LADM and MLADM techniques where the suggested scheme ELADM has proved accurate findings. The obtained results are graphically presented and are discussed. The convergence of ELADM technique is proved for solving nonlinear Volterra integral equation of second kind. The overall absolute error obtained acknowledges that the solutions by the proposed ELADM technique are very much similar to the exact solution. The suggested ELADM approach is thus easy to adopt, and the precision of the solution is clear.