Solving Bratu equations using Bell polynomials and successive differentiation

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 شهریور 1404   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.93423.1644

نویسنده

Niyazi Anil Gezer^*

Department of Mathematics, Faculty of Arts and Sciences, TED University, 06420, Ankara, Turkey.

چکیده

This paper uses transformations and recursive algebraic equations to obtain series expansions, utilizing Bell polynomials, to solve the one-dimensional Bratu problem and several Bratu-type equations. The central aim of this work is to compare this approach with the successive differentiation method (SDM) by using computer routines for the computation of Bell polynomials. The series expansion method is applied to this nonlinear ordinary differential equations, and the various aspects of computation are compared with those obtained by the SDM. The former method is effective in handling nonlinearity, especially those arising from exponential terms, and the complexity of computations involving exponentials is handled by readily available computer routines for Bell polynomials. On the other hand, the SDM needs to handle these complexities with each differentiation.

کلیدواژه‌ها

Successive differentiation method؛ Bratu equation؛ Computational analysis