AUTHOREA
Log in
Sign Up
Browse Preprints
LOG IN
SIGN UP
Essential Site Maintenance
: Authorea-powered sites will be updated circa 15:00-17:00 Eastern on Tuesday 5 November.
There should be no interruption to normal services, but please contact us at
[email protected]
in case you face any issues.
Devendra Kumar
Public Documents
1
An efficient parameter uniform spline-based technique for singularly perturbed weakly...
Satpal Singh
and 2 more
July 12, 2022
A parameter-uniform numerical scheme for a system of weakly coupled singularly perturbed reaction-diffusion equations of arbitrary size with appropriate boundary conditions is investigated. More precisely, quadratic $B$-spline basis functions with an exponentially graded mesh are used to solve a $\ell\times\ell$ system whose solution exhibits parabolic (or exponential) boundary layers at both endpoints of the domain. A suitable mesh generating function is used to generate the exponentially graded mesh. The decomposition of the solution into regular and singular components is obtained to provide error estimates. A convergence analysis is addressed, which shows a uniform convergence of the second order. To validate the theoretical findings, two test problems are solved numerically.