A new approximate analytical method for solving some non-linear initial value problems in physical sciences

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

Abstract

In this research study, one new approximate analytical method called Ananthaswamy-Sivasankari method for initial value problems is used to obtain the approximate solutions to some physical science problems, especially oscillator with fractional nonlinearities, duffing-harmonic oscillator, Helmholtz equation and some non-linear differential equations of oscillator analytically. The numerical and analytical solutions to these equations are then compared and the results indicate a good agreement. The explicit and closed form of derived approximate analytical solutions is given. The results explained that the new method is more convenient and easy to solve. Moreover, the outcomes are interlined graphically.

Published
2023-02-24