A Novel Iterative Method Based on Bernstein-Adomian Polynomials to Solve Non-Linear Differential Equations

摘要

In this paper, a new iterative formula for solving ordinary and partial nonlinear differential equations is derived based on the combination between Bernstein’s polynomial and the Adomian decomposition formula. The solution of the differential equations has been transformed into iterative formulas that find the solution directly without the need to convert it into a non-linear system of equations and solving it by other numerical methods that require considerable time and effort. The obtained results are compared with the exact solutions to show the efficiency and reliability of the proposed method which can be extended to solve a large variety of nonlinear differential equations. Tables are also given to show the variation of the absolute errors for larger approximation, namely for larger n.