Shilpkala T. Mane
Department of Applied Sciences, Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Lavale, Pune, 412115, Maharashtra, India. & Department of Engineering Sciences, SKNCOE, STES, Vadgaon, Pune, 411041, Maharashtra, India. E-mail: shilpkalajagtap8@gmail.com

Ram Kishun Lodhi
Department of Applied Sciences, Symbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University), Lavale, Pune, 412115, Maharashtra, India.

DOI https://doi.org/10.33889/IJMEMS.2025.10.4.056

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Abstract

In this paper, we developed an effective computational technique for addressing third-order linear singularly perturbed problems having the source term discontinuous. Boundary or interior layers are frequently present in singular perturbation issues, making traditional numerical techniques more challenging. Here, we present a quartic B-spline method (QBSM) for the approximate solution of the third-order singularly perturbed boundary value problem, improving both the accuracy and efficiency of the solutions. In addition, the proposed method's convergence and error are investigated. The performance of the current technique is demonstrated through numerous numerical tests. The numerical findings are compared to other approaches reported in the literature.

Keywords- Singularly perturbed problem, Reaction-diffusion type, Quartic B-spline method, Discontinuous source term, Truncation error.

Citation

T. Mane, S., & Lodhi, R. K (2025). Quartic B-Spline Technique for Third-Order Linear Singularly Perturbed Boundary Value Problem with Discontinuous Source Term. International Journal of Mathematical, Engineering and Management Sciences, 10(4), 1178-1191. https://doi.org/10.33889/IJMEMS.2025.10.4.056.