Parameter-uniform cubic spline method for singularly perturbed parabolic differential equation with large negative shift and integral boundary condition

Hailu, Wondimagegnehu Simon; Duressa, Gemechis File

doi:10.1080/27684830.2022.2151080

Cited by 9 publications

(1 citation statement)

References 27 publications

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“…This method computes highly accurate approximate solutions. Authors [18][19][20][21][22][23][24] also developed ε-uniform convergent numerical methods for singularly perturbed delay partial differential equation.…”

Section: Introductionmentioning

confidence: 99%

Parameter-uniformly convergent numerical scheme for singularly perturbed delay parabolic differential equation via extended B-spline collocation

Hassen,

Duressa

2023

Front. Appl. Math. Stat.

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This paper presents a parameter-uniform numerical method to solve the time dependent singularly perturbed delay parabolic convection-diffusion problems. The solution to these problems displays a parabolic boundary layer if the perturbation parameter approaches zero. The retarded argument of the delay term made to coincide with a mesh point and the resulting singularly perturbed delay parabolic convection-diffusion problem is approximated using the implicit Euler method in temporal direction and extended cubic B-spline collocation in spatial orientation by introducing artificial viscosity both on uniform mesh. The proposed method is shown to be parameter uniform convergent, unconditionally stable, and linear order of accuracy. Furthermore, the obtained numerical results agreed with the theoretical results.

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