Fitted reproducing kernel method for singularly perturbed delay initial value problems

2016 ◽  
Vol 284 ◽  
pp. 169-174 ◽  
Author(s):  
Z.Q. Tang ◽  
F.Z. Geng
Keyword(s):  
Initial Value Problems ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Singularly Perturbed ◽  
Initial Value ◽  
Reproducing Kernel Method

scholarly journals The Solution of a Class of Singularly Perturbed Two-Point Boundary Value Problems by the Iterative Reproducing Kernel Method

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Zhiyuan Li ◽  
YuLan Wang ◽  
Fugui Tan ◽  
Xiaohui Wan ◽  
Tingfang Nie
Keyword(s):  
Singular Perturbation ◽  
Boundary Layers ◽  
Present Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Perturbation Problems

In (Wang et al., 2011), we give an iterative reproducing kernel method (IRKM). The main contribution of this paper is to use an IRKM (Wang et al., 2011), in singular perturbation problems with boundary layers. Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate that the method is simple and effective.

scholarly journals Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yu-Lan Wang ◽  
Hao Yu ◽  
Fu-Gui Tan ◽  
Shanshan Qu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Perturbation Method ◽  
Present Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Singularly Perturbed ◽  
Partial Differential ◽  
Reproducing Kernel Method

We give the analytical solution and the series expansion solution of a class of singularly perturbed partial differential equation (SPPDE) by combining traditional perturbation method (PM) and reproducing kernel method (RKM). The numerical example is studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.

scholarly journals IMPLEMENTING REPRODUCING KERNEL METHOD TO SOLVE SINGULARLY PERTURBED CONVECTION-DIFFUSION PARABOLIC PROBLEMS

2021 ◽  
Vol 26 (1) ◽  
pp. 116-134
Author(s):  
Saeid Abbasbandy ◽  
Hussein Sahihi ◽  
Tofigh Allahviranloo
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
The Other ◽  
Singularly Perturbed ◽  
Parabolic Problems ◽  
Regular Boundary ◽  
Reproducing Kernel Method ◽  
Convection Diffusion ◽  
Linear And Nonlinear ◽  
Layer Behavior

In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved.

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