UTILIZATION OF DIFFERENTIAL TRANSFORMATION METHOD TO NONLINEAR THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

Jatin Kumar; Sunita; Anil Saini

doi:10.29121/shodhkosh.v5.i1.2024.2799

Authors

Jatin Kumar Assistant Professor, Department of Mathematics, Pt. C.L.S. Govt. College, Sec-14, Karnal, Haryana, India
Dr. Sunita Assistant Professor, Department of Mathematics, Niilm University, Kaithal, Haryana, India
Anil Saini Associate Professor, Department of Mathematics, M. D. Government GIRLS college Dadupur Roran karnal, Haryana, India

DOI:

https://doi.org/10.29121/shodhkosh.v5.i1.2024.2799

Keywords:

Differential Transformation Method, Singular Boundary Value Problems, Faa di Bruno's Formula, Nonlinearity, Numerical Analysis, Error Estimation, Reproducing Kernel Hilbert Space Method, Convergence Analysis, Mathematical Modeling

Abstract [English]

This paper explores the application of the Differential Transformation Method (DTM) to nonlinear three-point singular boundary value problems (SBVPs). The method incorporates "Faa di Bruno's formula," which utilizes "partial normal ring polynomials," to manage the nonlinearity of the equations. The paper presents error analysis results, comparing them with those obtained through other methods such as the reproducing kernel Hilbert space method (RKHSM). Numerical examples demonstrate the efficacy and reliability of the DTM in providing accurate solutions to these complex problems.

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