Numerical solution of Bernoulli and Lane Emden type differential equation by Laplace-Adomian technique

Itishree Sahu; Satyajit Mohapatra; Saumya Ranjan Jena; Archana Senapati

Itishree Sahu Dept of Mathematics, School of Applied Sciences,\\ KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India.
Satyajit Mohapatra KIIT, Polytechnic,\\ KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India.
Saumya Ranjan Jena Dept of Mathematics, School of Applied Sciences,\\ KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India.
Archana Senapati Dept of Mathematics,\\ Centurion University, R. Sitapur, Paralakhemundi, Gajapati-761211, Odisha, India

Abstract

In this study, we have employed the Laplace transform method with Newton-Raphson based Adomian decomposition to investigate the approximate solution for first and second order ordinary differential equation like Bernoulli Differential equation and Lane Emden type differential equation. The inverse Laplace transform is implemented to obtain the solution. The effectiveness of the method is illustrated through four numerical examples. The numerical results of the examples are explored through two-dimensional plot which show the
applicability of the presented approach. The results of this study evident that the suggested methods for studying ordinary differential equation is efficient and reliable.