A High Accurate Numerical Solution Method For Fredholm Integral Equations With Semi-smooth Kernels

This thesis is concerned with numerical solution methods for Fredholm integral equations of the second kind with semi-smooth kernels and numerical quadratures based on nonlinear variable substitutions.For integral equations with semi-smooth kernel, some numerical solution methods need to continue the kernel function. In general, natural continuation is adopt, which may cause large rounding-off error for some problems. There-fore, we seek new continuation method to avoid this problem. By using the new continuation method, the accuracy of numerical solutions can be improved considerably.This thesis is also concerned with numerical quadratures for two types of integrals. In the first type of integrals, it is assumed that the integration interval [a,b] (b> a) is very large, and the integrand varies quickly near the end a while it varies very slow near the end b. In the second type of integrals, the integration interval is infinite. Suitable nonlinear variable substitutions are introduced for these integrals to obtain high accurate numerical quadratures. Numerical results' are given to illustrate the accuracy of the proposed quadratures.