ABSTRACT
Many numerical methods are available in the literature and the very popular finite difference method. With this method, a particular differential equation is replaced with a difference equation, that is, a system of linear equations that can be solved by a computer. The object of the Euler's method is to obtain an approximation to the initial value problem. The second order Runge-Kutta method is also known as the improved Euler's method. The spectral element method represents a special case of Galerkin methods in which the finite dimensional space of test functions is made of continuous piecewise algebraic polynomials of high degree on each element of a partition of the computational domain. For ease of exposition, the chapter focuses on the one-dimensional problem. Numerical Methods are used to solve problems in the oil industry and other fields.
