Related Experiment Video
Updated: Jul 26, 2025

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
Published on: August 30, 2019
A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift
Ababi Hailu Ejere1, Tekle Gemechu Dinka2, Mesfin Mekuria Woldaregay2
1Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. hailu_ababi@yahoo.com.
Objective:
The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the perturbation parameter, and the term with negative shift causes interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically. We have treated the problem by proposing a numerical scheme using the implicit Euler method in the temporal direction and a fitted tension spline method in the spatial direction with uniform meshes.
Result:
Stability and uniform error estimates are investigated for the developed numerical scheme. The theoretical finding is demonstrated by numerical examples. It is obtained that the developed numerical scheme is uniformly convergent of order one in time and order two in space.
More Related Videos
12:15Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
Published on: April 9, 2019
06:45Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
Published on: October 28, 2022
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Thermal Sigmatropic Reactions: Overview
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
Second Order systems II
Root Loci for Positive-Feedback Systems
The construction rules for the root locus in positive feedback systems are similar to those in...
Le Chatelier's Principle: Changing Concentration
Statically Indeterminate Problem Solving