Second-Order Robust Numerical Method for a Partially Singularly Perturbed Time-Dependent Reaction-Diffusion System

Article Engineering, Multidisciplinary

Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects

Hardik Joshi et al.

Summary: Calcium signaling in nerve cells is crucial for brain functions, and a fractional-order mathematical model is used to study the spatiotemporal profile of calcium. Calbindin-D-28k affects the distribution of calcium and plays a role in cell memory and toxicity.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION (2023)

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Article Mathematics, Applied

2D memory-based mathematical analysis for the combined impact of calcium influx and efflux on nerve cells

Hardik Joshi et al.

Summary: In this paper, a calcium dynamics model is proposed to study cellular activities and calcium homeostasis by considering the exchange of calcium flux between intracellular and extracellular sources. A generalized two-dimensional reaction-diffusion model is formulated and analyzed for different ranges of calcium flux. The model is solved using the fractional integral transform and special functions, and the existence and uniqueness of the proposed model are discussed. The obtained results are graphically presented to illustrate the significance of calcium flux and validate the effectiveness of the method.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2023)

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Article Mathematics, Applied

Higher order computational method for a singularly perturbed nonlinear system of differential equations

Manikandan Mariappan et al.

Summary: This article discusses a boundary value problem for a nonlinear system of singularly perturbed two second order differential equations, where only the first equation is multiplied by a small positive parameter. A numerical method utilizing a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested to solve the system, showing essentially second order convergence in the maximum norm uniformly with respect to the perturbation parameter. Numerical illustrations provided support the theoretical results.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2022)

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Article Mathematics, Applied