Журнал прикладной и вычислительной математики

Recurrence Relation When Solving 2^nd Order Homogeneous Linear ODEs by Frobenius Method

Abstract

Saad F. Shaikh

The Frobenius method, also known as the Extended Power Series method comes into play when solving second-order homogeneous linear ODEs having variable coefficients, about a singular point. The solution is expressed in terms of infinite power series. This straightforward article is merely aimed to lucidly arrive at the recurrence relation/formula by taking proper heed of summation limits and simply manipulating them, which is probably absent in almost all research articles and books. The methodology discussed is followed by a few conspicuous and relevant observations.