ANALYSIS OF VARIOUS METHODS TO OBTAIN SERIES SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS OF SECOND ORDER WITH VARIABLE COEFFICIENTS AND MODIFICATION IN FROBENIUS METHOD


By

Anil Maheshwari and Adarsh Mangal 

Engineering College Ajmer, Rajasthan, India - 305001 

Email: anil.knowledge@gmail.com, dradarshmangal1@gmail.com 

(Received: March 25 , 2024 , In format: April 07 , 2024;  Revised: May 22 , 2024; Accepted: June 09 , 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54137



Abstract

This research paper presents a comprehensive comparison of various methods employed for obtaining series solutions to second-order ordinary differential equations featuring variable coefficients with only complementary functions. The primary focus lies on evaluating the efficacy and applicability of these methods in handling the complexities inherent in solving such differential equations in series. Through rigorous analysis and various examples, the strengths and limitations of each approach are delineated, shedding light on their comparative performance in terms of computational efficiency. Furthermore, this paper proposes modification to the traditional Frobenius method, tailored to address specific challenges encountered when dealing with variable coefficients. 


2020 Mathematical Sciences Classification: 34A99, 34D06, 97I99. 

Keywords and Phrases: Series solution, Power series method, General method, Frobenious method, Ordinary point, Singular point. 

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