2013/10/07 by Kourosh Parand, Parand, K., Jamal Amani Rad +2
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fractional Differential Equations Solutions #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1310.1906
openalex publication_date 2013/10/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The objective of this paper is to apply the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs versus ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs and the differential equations solved by them do not have high-degree nonlinearity and the reported results are not regarded as appropriate criteria for the excellence of the new method. So, we chose Emden-Fowler type differential equations and solved them by this method. To confirm the accuracy of the new method and to show the preeminence of EOMs versus OOMs, the norm1 of the residual and error function of both methods are evaluated for multiple m values, where m is the degree of the Bernstein polynomials. We reported the results in form of plots to illustrate the error convergence of both methods to zero and also to show the primacy of the new method versus OOMs. The obtained results have demonstrated the increased accuracy of the new method.