A new approximate analytical method (ASM) for solving some non-linear boundary value problems

Vembu Ananthaswamy; S. Sivasankari; Seenith Sivasundaram

Vembu Ananthaswamy The Madura College, Madurai, Tamil Nadu, India.
S. Sivasankari Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India
Seenith Sivasundaram College of Science, Engineering and Mathematics, Daytona Beach, Florida 321114, USA

Abstract

The analysis of non-linear differential equations is discussed in this study using a new, straight-forward method that is also incredibly precise. The new method is illustrated with certain examples, which makes it easier to understand. The accuracy of the approximate analytical solutions obtained is checked by comparison with numerical solutions, exact solutions and other approximate analytical methods with significant agreement. The results demonstrate that this method is most effective, simple and convenient. The results obtained are explained graphically and analytically. It is simple to adapt this approach to address more non-linear boundary value issues in the physical, chemical, and biological sciences.