Applications of Quintic Hermite collocation with time discretization to singularly perturbed problems

作者：Arora Shelly; Kaur Inderpreet^*

来源：Applied Mathematics and Computation, 2018, 316: 409-421.

DOI：10.1016/j.amc.2017.08.040

• Singular perturbation
• Quintic Hermite collocation
• Forward difference
• Parameter uniform convergence
• Collocation points

Singular perturbation problems have been discussed using collocation technique with quintic Hermite interpolating polynomials as base functions. These polynomials have the property to interpolate the function as well as its tangent at node points. To discretize the problem in temporal direction forward difference operator has been applied. The given technique is a combination of collocation and difference scheme. Parameter uniform convergence has been studied using the method given by Farrell and Hegarty (1991). Rate of convergence of quintic Hermite difference scheme has been found to depend upon node points. Applicability and computational effect of the scheme has been examined through numerical examples. Results have been presented graphically through surface plots as well as in tabular form.

• 出版日期2018-1-1