论文标题
半线性奇异反应扩散边界值问题的全局数值解决方案
On construction of a global numerical solution for a semilinear singularly--perturbed reaction diffusion boundary value problem
论文作者
论文摘要
构建了一类不同的方案，用于构建了半线性奇异的反应边界的数值求解。证明了差异方案的稳定性，并显示了数值解决方案的存在和独特性。之后，已经证明了相对于扰动参数$ \ varepsilon $在修改后的Shishkin网格上的均匀收敛。对于这样的离散解决方案，构建了基于线性样条的全局解决方案，此解决方案的误差也在预期的边界中。论文末尾的数值实验，确认理论结果。基于天然立方样条的全球溶液以及Liseikin，Shishkin和改良Bakhvalov网格的实验也包括在数值实验中。
A class of different schemes for the numerical solving of semilinear singularly--perturbed reaction--diffusion boundary--value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of a numerical solution were shown. After that, the uniform convergence with respect to a perturbation parameter $\varepsilon$ on a modified Shishkin mesh of order 2 has been proven. For such a discrete solution, a global solution based on a linear spline was constructed, also the error of this solution is in expected boundaries. Numerical experiments at the end of the paper, confirm the theoretical results. The global solutions based on a natural cubic spline, and the experiments with Liseikin, Shishkin and modified Bakhvalov meshes are included in the numerical experiments as well.
