ABSTRACT
The order of the differential equation is equivalent to the order of the highest derivative in the equation; for example, an equation that includes only first and second derivatives would be a second-order differential equation. An equation that defines a relationship between an unknown function and one or more of its derivatives is referred to as a differential equation. Differential equations can originate from either geometric or physical problems. Physical problems can also be defined by differential equations. Simple problems in electrical circuits and heat transfer are commonly used to introduce differential equations. Simple motion problems can also be governed by differential equations. Errors in numerical solutions of differential equations can be classified as global or local errors. The local errors occur over one step size, whereas the global errors are cumulative over the range of solution. Many engineering problems require the solution of higher order differential equations.
