Power Series Method applied to Inverse Analysis in Chemical Kinetics Problem

TL;DR

This paper extends the power series solution method to nonlinear partial differential equations, specifically Burgers-Type equations, demonstrating its broader applicability beyond linear cases.

Contribution

It introduces the use of power series for solving nonlinear PDEs, expanding the method's application scope in chemical kinetics and differential equations.

Findings

Successfully applied to three Burgers-Type equations

Demonstrates effectiveness for nonlinear PDEs

Shows potential for inverse analysis in chemical kinetics

Abstract

Power Series Solution Method has been traditionally used to solve Ordinary and Partial Linear Differential Equations. However, despite their usefulness the application of this method has been limited to this particular kind of equations. In this work we use the method of power series to solve nonlinear partial differential equations. The method is applied to solve three versions of nonlinear time-dependent Burgers-Type differential equations in order to demonstrate its scope and applicability.