MUMBAI, India, Oct. 5 -- Intellectual Property India has published a patent application (202611101888 A) filed by Manipal University Jaipur on August 24, 2026, for An Efficient Spline-Based Method For Two-Parameter One-Dimensional Parabolic Singularly Perturbed Systems With Time Delay And Unequal Diffusion Parameters.
Inventor includes Dr. Parvin Kumari.
The application for the patent was published on October 02, 2026, under issue no. 40/2026.
Abstract: The present invention relates to an efficient spline-based method for two-parameter one-dimensional parabolic singularly perturbed systems with time delay and unequal diffusion parameters. The method employs CrankâNicolson time discretization on a uniform temporal mesh and B-spline-based spatial approximation on a specially designed nonuniform Shishkin mesh. The Shishkin mesh efficiently resolves sharp and overlapping boundary layers caused by singular perturbations, while the B-spline approximation enhances spatial accuracy and solution smoothness, thereby providing a stable and accurate numerical solution for delayed parabolic systems. The completely discrete scheme demonstrates uniformly convergent method with about second-order convergence in space and second-order convergence in time. In reality, higher-order numerical approaches are used because they may provide precise numerical approximations at a negligible extra processing cost. To support the positive aspects of the numerical approach, several test problems are taken into consideration. The test cases' numerical results unequivocally demonstrate the numerical method's uniform convergence rate and efficiency, which are in line with the theoretical findings.
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