A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems

Authors

  • M. Zahurul Islam Department of Applied Mathematics, Rajshahi University, Rajshahi-6205, Bangladesh
  • M. Shamsul Alam Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi-6204, Bangladesh
  • M. Bellal Hossain Department of Mathematics, Rajshahi University of Engineering and Technology, Rajshahi-6204, Bangladesh

DOI:

https://doi.org/10.15625/0866-7136/30/1/5607

Abstract

A general asymptotic solution is presented for investigating the transient response of non-linear systems modeled by hyperbolic-type partial differential equations with small nonlinearities. The method covers all the cases when eigen-values of the corresponding unperturbed systems are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the eigen-values in the general result that the solution corresponding to each of the three cases can be obtained. The method is an extension of the unified Krylov-Bogoliubov-Mitropolskii method, which was initially developed for un-darnped, under-clamped and over-clamped cases of the second order ordinary differential equation. The methods also cover a special condition of the over-damped case in which the general solution is useless.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

31-03-2008

How to Cite

Islam, M. Z., Alam, M. S., & Hossain, M. B. (2008). A unified Krylov-Bogoliubov-Mitropolskii method for solving hyperbolic-type nonlinear partial differential systems. Vietnam Journal of Mechanics, 30(1), 11–19. https://doi.org/10.15625/0866-7136/30/1/5607

Issue

Section

Research Paper