## Numerical Solutions to Ordinary Differential Equations

We will discuss the following methods:

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## Numerical Integration

Techniques of numerical integration have been developed because of the following reasons:

1. Integration, in general, is a difficult operation.
2. We may have experimental data, but we may not know the actual function generating those values.

In this article, we will discuss 3 commonly used numerical integration techniques, the trapezoidal rule, Simpson’s 1/3rd rule and Simpson’s 3/8th rule.

## Trapezoidal Rule

• Uses the single degree curve for integration

## Simpson’s 1/3rd Rule

This rule is also known as Simpson’s rule.

• Uses a second degree curve for integration.

## Simpson’s 3/8th Rule

• It uses a third degree curve for integration