An application of Bell polynomials in numerical solving of nonlinear differential equations

2019/01/27 by Josef Rebenda, Rebenda, Josef
Mathematics · #34A45 34A25 34A34 05A19 26E05 #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1901.10418

openalex publication_date 2019/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Partial ordinary Bell polynomials are used to formulate and prove a version of the Faà di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two examples of solving the initial value problem for differential equations which are nonlinear with respect to the dependent variable.

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