Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Abstract
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In fact, a set of uniform centers is distributed in the computational domain, and then coordinate stretching based transform is used to move the centers, to the region with high gradients. In addition to the integrated multiquadric (MQ) collocation method is applied to solve the transformed equation. The effectiveness of our method is demonstrated on several examples with boundary layer in both cases, i.e., boundary layer on the left side as well as the right side.
Akhavan Ghassabzade, F., Saberi_Nadjafi, J., & Soheili, A. R. (2018). A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers. Computational Methods for Differential Equations, 6(3), 295-311.
MLA
Fahimeh Akhavan Ghassabzade; Jafar Saberi_Nadjafi; Ali Reza Soheili. "A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers". Computational Methods for Differential Equations, 6, 3, 2018, 295-311.
HARVARD
Akhavan Ghassabzade, F., Saberi_Nadjafi, J., Soheili, A. R. (2018). 'A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers', Computational Methods for Differential Equations, 6(3), pp. 295-311.
VANCOUVER
Akhavan Ghassabzade, F., Saberi_Nadjafi, J., Soheili, A. R. A method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers. Computational Methods for Differential Equations, 2018; 6(3): 295-311.
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