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FST Math Research: A simple solution for a complicated problem

Mathphobia is a common thing among students who often see the subject as overly technical. Because of this there is an ever-growing need to find simple ways to solve and present complicated mathematical problems. That is exactly what Dr. Mahesha Narayana (Dept. of Mathematics) and colleagues in India have done in their paper titled “On the differential transform method of solving boundary eigenvalue problems: An illustration’ which was recently published in the ZAMM‐Journal of Applied Mathematics and Mechanics. In their paper they use a simple technique to arrive at the solution of a complicated problem.


The paper explains how a simple transform technique (a ‘transform’ helps in converting a difficult task into an easier one) based on the Taylor series method can be used to solve a boundary eigen value problem (BEVP), subject to general boundary conditions, arising from a fluid dynamics problem. A Taylor series is an infinite power series of a continuous function that helps in approximating the eigen solution of the BEVP of interest. In the authors’ technique, the boundary value problem (BVP) is first converted into an initial value problem (IVP) by replacing the right-end boundary conditions using initial guess conditions and also treating the eigenvalue as an additional unknown to obtain the recurrence relations between the coefficients of the Taylor series. An additional artificial differential equation and a normalization condition are used for closure, and the guess values together with the eigenvalue are solved using a well-known numerical method called the Newton-Raphson.


Even if some of the terms above are a little unfamiliar, what is significant about the study is its simplicity. When other methods of solution fail, this method works, and it takes very few terms to get a good approximation of the desired solution. Furthermore, the method has been over-simplified in the study to make it easy for even the less computer-savvy person to comfortably implement it on a computer. With no great algorithms to learn, the method is so elegant that a high school student with little mental exertion and with the necessary guidance can follow it. The authors are convinced that the simplicity of the method in obtaining a reliable solution to a BEVP will help create interest in Mathematics among Jamaican students and pave the way for using other such simple techniques to handle challenging problems. “Believe us” they note “Mathematics is for everyone!” We believe them!


To read the paper: M. Narayana, M. Shekar, P.G. Siddheshwar, N.V. Anuraj. On the differential transform method of solving boundary eigenvalue problems: An illustration, Z Angew Math Mech. 2020, e202000114.


To learn more about research in the Department of Mathematics:

Published on 10 Mar, 2021

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