Numerical inverse Laplace transform based on Bernoulli polynomials operational matrix for solving nonlinear differential equations

Abstract

A numerical inverse Laplace transform method is established using Bernoulli polynomials operational matrix of integration. The efficiency of the method is demonstrated through some standard nonlinear differential equations: Duffing equation, Van der Pol equation, Blasius equation and jerk equation. The solution approach is to adopt Laplace Adomian decomposition method for solving nonlinear differential equations and then at each step employ the numerical inverse Laplace transform using the developed method based on Bernoulli polynomials operational matrix of integration. The numerical results exemplify that the estimated solutions are in good agreement with exact or numerical methods available in literature wherever the exact solutions are not known.