Series solution of nonlinear differential equations by a novel extension of the Laplace transform method

Abstract

A technique for extending the Laplace transform method to solve nonlinear differential equations is presented. By developing several theorems, which incorporate the Adomian polynomials, the Laplace transformation of nonlinear expressions is made possible. A number of well-known nonlinear equations including the Riccati equation, Clairaut's equation, the Blasius equation and several other ones involving nonlinearities of various types such as exponential and sinusoidal are solved for illustration. The proposed approach is analytical, accurate, and free of integration.

Keywords:

• Laplace transform method
• nonlinear differential equations
• Adomian polynomials

2010 AMS Subject Classifications:

• 44A10
• 34-XX
• 35-XX
• 34G20

Acknowledgements

We (H.F. and H.A) are obliged to the editor and anonymous reviewers of the IJCM for their valuable comments which helped us improve the quality of the initial draft of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.