Boundary value analysis and Equivalence partitioning, explained with simple example:

Boundary value analysis and equivalence partitioning both are test case design strategies in black box testing.

Equivalence Partitioning:

In this method the input domain data is divided into different equivalence data classes. This method is typically used to reduce the total number of test cases to a finite set of testable test cases, still covering maximum requirements.

In short it is the process of taking all
possible test cases and placing them into classes. One test value is
picked from each class while testing.

E.g.: If you are testing for an input box accepting
numbers from 1 to 1000 then there is no use in writing thousand test
cases for all 1000 valid input numbers plus other test cases for
invalid data.

Using equivalence partitioning method above test cases can be
divided into three sets of input data called as classes. Each test case
is a representative of respective class.

So in above example we can divide our test cases into three equivalence classes of some valid and invalid inputs.

Test cases for input box accepting numbers between 1 and 1000 using Equivalence Partitioning:
1) One input data class with all valid inputs. Pick a
single value from range 1 to 1000 as a valid test case. If you select
other values between 1 and 1000 then result is going to be same. So one
test case for valid input data should be sufficient.

2) Input data class with all values below lower limit. I.e. any value below 1, as a invalid input data test case.

3) Input data with any value greater than 1000 to represent third invalid input class.

So using equivalence partitioning you have categorized all possible
test cases into three classes. Test cases with other values from any
class should give you the same result.

We have selected one representative from every input class to design
our test cases. Test case values are selected in such a way that
largest number of attributes of equivalence class can be exercised.

Equivalence partitioning uses fewest test cases to cover maximum requirements.

Boundary value analysis:

It’s widely recognized that input values at the extreme ends of input domain cause more errors in system. More application errors occur at the boundaries of input domain. ‘Boundary value analysis’ testing technique is used to
identify errors at boundaries rather than finding those exist in center
of input domain.

Boundary value analysis is a next part of Equivalence partitioning
for designing test cases where test cases are selected at the edges of
the equivalence classes.

Test cases for input box accepting numbers between 1 and 1000 using Boundary value analysis:
1) Test cases with test data exactly as the input boundaries of input domain i.e. values 1 and 1000 in our case.

2) Test data with values just below the extreme edges of input domains i.e. values 0 and 999.

3) Test data with values just above the extreme edges of input domain i.e. values 2 and 1001.

Boundary value analysis is often called as a part of stress and negative testing.

Note: There is no hard-and-fast rule to test only
one value from each equivalence class you created for input domains.
You can select multiple valid and invalid values from each equivalence
class according to your needs and previous judgments.

E.g. if you divided 1 to 1000 input values in valid
data equivalence class, then you can select test case values like: 1,
11, 100, 950 etc. Same case for other test cases having invalid data
classes.

This should be a very basic and simple example to understand the Boundary value analysis and Equivalence partitioning concept.

(Source: Internet - From Indian's blog ^_^)