Abstract: A smooth solution of the first order nonlinear hyperbolic partial differential equation arising in transport phenomena is discussed. Although the method of characteristics is offered within the literature, it conjointly comes across some difficulties like it is valid only for first order hyperbolic partial differential equations[PDEs], converts the PDE into family of ordinary differential equations[ODEs] (may be difficult, especially if there is coupling between the equations) and solution cannot be obtained always explicitely. To avoid such complexities, in this paper, we have a tendency to propose proficient analytical method namely the reduced differential transform method [RDTM] to solve above mentioned equation. In order to show the efficiency of the proposed method we use the iterative Laplace transform method [ILTM]. The result's conferred in the form of power series. We complete a couple of numerical illustrations so as to ensure a few points of interest of the RDTM over ILTM that reveals that the ILTM concedes the noise terms in each iterative process that prompts utilization of additional time and it's a blend of two schemes, especially, Laplace transform and iterative techniques whereas such difficulties aren't there in RDTM. Besides, we tend to perform numerical simulation through matlab version R2012a. Furthermost, we present convergence analysis of RDTM.

Keywords: Reduced differential transform method, Iterative Laplace transform method, Noise terms.

 

DOWNLOAD PDF          DOWNLOAD XML

 

How to cite this article:

A. Saravanan, N. Magesh and A. John Christopher, A new computational method for smooth solution of first order nonlinear Cauchy problem,  International Journal of Advances in Mathematics, Volume 2018, Number 5, Pages 14-24, 2018.