Question

as described in sec. 9.5, linear algebraic equations can arise in the solution of differential equations via finite-difference approximations. for example, the following differential equation results from a steady-state mass balance for a chemical in a stream along the axis of flow, x:

Answer 1

Linear algebraic equations can arise in the solution of differential equations through finite-difference approximations. In the context of a steady-state mass balance for a chemical in a stream along the axis of flow, the resulting differential equation is d²I(x)/dx² = 0. This equation represents a second-order linear differential equation involving the function I(x) and its second derivative with respect to x.

Step-by-step explanation:

Linear algebraic equations can arise in the solution of differential equations through finite-difference approximations. In the context of a steady-state mass balance for a chemical in a stream along the axis of flow, we can obtain the following differential equation:

d²I(x)/dx² = 0

This equation represents a second-order linear differential equation. It describes a situation where the second derivative of the function I(x) with respect to x is equal to zero, indicating a constant rate of change along the x-axis. This equation can then be solved using algebraic methods to find the solution, I(x), that satisfies the given boundary conditions.