摘要
本论文主要讨论了一类含双参数半线性常微分方程、一类具有转向点的椭圆型方程、半线性抛物型方程、二维半线性抛物型方程和双曲-抛物型偏方程奇摄动问题的数值解, 首先给出这些方程解的导数估计, 然后对不同问题构造了不同的差分格式, 最后我们证明了该差分格式关于小参数一致收敛.
In this dissertation, the numerical solution of singularly perturbed problems for a class of Semilinear ordinary equations involving two parameters, a class of elliptic equations with turning points, a Semilinear parabolic equation, and a two level Semilinear parabolic equation as well as a hyperbolic-parabolic partial differential equation are mainly considered. The bounds on the derivatives of these exact solutions are given. Then different difference schemes are constructed for different problems. Finally, we prove the uniform convergence on the small parameterfor these difference schemes.
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