Chapter 2.8, Problem 8E

Interpretation Introduction

Interpretation:

To show that the local error of modified Euler’s method is proportional to ${\text{(Δt)}}^{\text{3}}$.

Concept Introduction:

Local error is an error in particular interval say $\text{x+ξ and x-ξ}$.

As we know, the simple Euler method for numerical integration uses slope at the single function point to find the next point. This might be a problem for larger intervals $\text{Δt}$. This can be overcome by using a modified Euler’s method. It finds out the average slope between ${\text{x}}_{\text{n}}$ and ${\text{x}}_{\text{n+1}}$ thus has a lower error.