Abstract
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.
Highlights
Perturbed problems (SPPs) arise very frequently in many branches of mathematics such as fluid mechanics and chemical reactor theory
Many papers [1,2,3,4] are devoted to SPPs of ordinary differential equation and the authors discussed the situation and width of boundary layer(s) and give some effective numerical algorithms
Few papers [5,6,7] deal with singularly perturbed partial differential equation (SPPDE)
Summary
Perturbed problems (SPPs) arise very frequently in many branches of mathematics such as fluid mechanics and chemical reactor theory. It is well known that the solutions of SPPs exhibit a multiscale character. Few papers [5,6,7] deal with SPPDE. The reproducing kernel Hilbert function space has been shown in [8,9,10] to solve a large class of linear and nonlinear problems effectively. We solve a class of SPPs in reproducing kernel space. By using a traditional perturbation method and RKM, the series expansion solution of a class of SPPDE is given. The main contribution of this paper is to use RKM in SPPDE. The reason why we use this method is that we aim to solve some problems in many areas of science and improve high precision. It is quite well known that solution of such problems involves boundary layers
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