Numerical Solution Of Singularly Perturbed Problems

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.