This paper introduces a procedure to apply Laplace transform theory in solving a class of Sturm – Liouville boundary – value problems, namely those having polynomial coefficients. The method demonstrates that not only can Laplace transforms solve differential equations satisfying only initial-value conditions, but can also be adaptable to solving boundary – value problems. In the end, the application of inverse Laplace transforms to the problem introduces the reader to a novel approach in the analysis and solution of a specific class of Sturm – Liouville boundary problems.
Roberto P. Briones (2021); Some Notes on the Solution of Sturm-Liouville Boundary-Value Problems Having Polynomial Coefficients using Laplace Transforms; International Journal of Scientific and Research Publications (IJSRP)
11(6) (ISSN: 2250-3153), DOI: http://dx.doi.org/10.29322/IJSRP.11.06.2021.p11425