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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Weiqun Zhang
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DOI:10.17265/2159-5291/2019.01.001
Lake Campus Science & Mathematics, Wright State University, 7600 State Rt 703, Celina, OH 45822, USA
A numerical method using weak formulation is proposed to solve singularly perturbed differential equations. The numerical method is applied to both linear and nonlinear perturbation problems. A linear differential equation is solved using its weak formulation with a test space composed of exponential functions matching boundary layers. A nonlinear singular perturbation problem is converted into a system of linear differentiation equations. Then each linear differential equation is solved iteratively. The uniform convergence, which is independent of the singular perturbation parameter, is numerically verified.
Singular perturbation, differential equations, boundary layers, numerical methods, weak formulation.
Weiqun, Z. 2019. "A Uniformly Convergent Numerical Method Using Weak Formulation for Singularly Perturbed Differential Equations." Journal of Mathematics and System Science 9: 1-6.
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