In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturba...In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturbation parameter. The proposed method uses interval analysis principle to deal with the uncertain parameter and the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Furthermore, sensitivity analysis has been conducted using different methods to assess how much the solution is sensitive to the changes of the perturbation parameter. Numerical results are provided to show the applicability and efficiency of the proposed method, which is ε-uniform convergence of almost second order.展开更多
文摘In this paper, we develop a new numerical method which is based on an exponential spline and Shishkin mesh discretization to solve singularly perturbed boundary value problems, which contain a small uncertain perturbation parameter. The proposed method uses interval analysis principle to deal with the uncertain parameter and the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Furthermore, sensitivity analysis has been conducted using different methods to assess how much the solution is sensitive to the changes of the perturbation parameter. Numerical results are provided to show the applicability and efficiency of the proposed method, which is ε-uniform convergence of almost second order.
基金Supported by the National Natural Science Funds(11071075)the Natural ScienceFoundation of Shanghai(10ZR1409200)the National Laboratory of Biomacromolecules,Institute of Biophysics,Chinese Academy of Sciences,the E-Institutes of Shanghai Municipal Education Commissions(E03004)
