Applied Engineering Analysis

Chapter 10Numerical Solution Methods for Engineering Analysis

Chapter Learning Objectives

• Learn the alternative ways of using numerical methods to solve nonlinear equations, perform integration, and solve differential equations.
• Learn the principles of various numerical techniques for solving nonlinear equations, performing integrations, and solving differential equations by the Runge–Kutta methods.
• Learn the fact that numerical methods offer approximate but credible accurate solutions to the problems that are not readily or possibly solved by closed-form solution methods.
• Learn the fact that numerical solutions are available to the users only at the preset solution points, and the accuracy of the solutions is largely dependent on the size of the increments of the variable selected for the solutions.
• Become familiar with the value of commercially available numerical solution software packages such as Mathematica and MatLAB.

10.1 Introduction

Numerical methods are techniques for solving the mathematical problems involved in engineering analysis that cannot be solved by closed-form solution methods such as those presented in the preceding chapters. In this chapter, we will learn the use of some of the available numerical methods that will not only enable engineers to solve many mathematical problems, but also allow engineers to minimize the need for the many hypotheses and idealization of the conditions, such as those stipulated in Section 1.4.

Numerical techniques have ...