Solving Bratu equations using Bell polynomials and successive differentiation

Document Type : Research Article

Author

• N.A. Gezer

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

10.22067/ijnao.2025.93423.1644

Abstract

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 these 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. 

Keywords

• Successive differentiation method
• Bratu equation
• Computational analysis

Main Subjects

• Numerical methods for differential equations and its applications

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