Non-Linear Equations (Mathematical Analysis for Scientists & Engineers Book 4)

This unit, Series No. 4, deals with non-linear equations. For many readers, this may be an entirely novel area of study. Several instances of non-linear equations are encountered in the sciences and engineering. They are solved primarily by iterative methods, which include the incremental search method, the bisection method, the Newton-Raphson method, and the Secant method. These methods are described along with their limitations individually. The need for curve sketching for approximate location of the roots of a non-linear equation is emphasized even when computer software functions are to be employed for accurate determination of the root(s). For the solution of systems of equations that include non-linear equations, a Gauss-Seidel type of iterative method of solution with relaxation is described together with strategies for achieving rapid convergence.