An effective numerical approach for two parameter time-delayed singularly perturbed problems

A Numerical Approach for Diffusion‐Dominant Two‐Parameter Singularly Perturbed Delay Parabolic Differential Equations

“…Te numerical solution in [34] compared the error and convergence rate of problem 1, when ε � 10 − 4 and μ � 10 − 9 for mesh grid 64 ≤ N � 4M ≤ 512, with the prior literature results of [32,33]. We also include our numerical out comes in comparison with these prior results in Table 7.…”

“…Te concern of our problem is a two-parameter singularly perturbed time delay one-dimensional parabolic diferential equation for the given initial and two boundary conditions. Diferent numerical methods of this type of problems are studied by some authors [31][32][33][34]. Govindarao and others in [31] solved the problem by applying implicit Euler fnite diference approximation on uniform mesh in the direction of time and upwind fnite diference approximation on Shishkin and Bakhvalov-Shishkin mesh in space direction.…”

“…Recently, two articles entitled "An efective numerical approach for two-parameter timedelayed singularly perturbed problems" and "Fitted cubic spline scheme for two-parameter singularly perturbed timedelay parabolic problems" also addressed this problem. Te frst article applied the Crank-Nicolson scheme in temporal direction and the B-spline collocation method for spatial [33] and the second article applied a combination of the ftted operator scheme of a cubic spline with θ-method on a uniform mesh grid [34].…”