Numerical methods for solving ordinary and partial differential equations have always been important in scientific investigations. With the advent of computers, the use of numerical methods has been popularized, and more importantly, people are now able to tackle those problems which are fundamental to our understanding of scientific phenomena, but were so much more difficult to study in the past. Spectral methods is the name given to a numerical approach for the solution of differential, integral and integro equations. Our intension in this book is to develop formulas which are new to the best of our knowledge; for the generation of higher order pseudospectral integration matrices. This is used for solving integral and ordinary differential equation applying the proposed formulas transforms the linear integral equation into a system of linear equations which can be solved using any of the well-known numerical methods.