Recurrence relation is a mathematical equation or formula that expresses the time complexity of a recursive algorithm in terms of its subproblem sizes. It describes the relationship between the input size and the number of operations performed by the recursive algorithm.

To analyze the time complexity of a recursive algorithm using recurrence relations, you typically follow these steps:

1. Identify the Subproblems: Determine how the problem is divided into smaller subproblems during each recursive call. Identify the size of the subproblems and any parameters that affect the problem size.
2. Formulate the Recurrence Relation: Express the time complexity of the algorithm using a mathematical equation. The equation should relate the time taken to solve a problem of size 'n' with the time taken to solve its subproblems of smaller sizes.
3. Determine the Base Case Complexity: Identify the time complexity of the base case(s) of the recursion. This represents the simplest version of the problem that can be solved directly.
4. Solve the Recurrence Relation: Solve the recurrence relation to obtain an explicit formula or a tight asymptotic bound for the time complexity. Techniques like substitution, iteration, recursion trees, or master theorem may be used depending on the nature of the recurrence relation.
5. Analyze the Resulting Time Complexity: Determine the overall time complexity of the recursive algorithm based on the solution of the recurrence relation. Express the time complexity using Big O notation or a similar notation that captures the growth rate of the algorithm.

It's important to note that solving recurrence relations can be complex and may require mathematical analysis or the application of specific techniques for different types of relations (linear, divide and conquer, etc.). In some cases, the time complexity may be a direct result of the number of recursive calls and the work done at each level.

Additionally, it's crucial to consider any overhead or additional work performed outside of the recursive calls, such as initialization, merging results, or other non-recursive operations. These factors may influence the overall time complexity of the algorithm.

Recurrence relations provide a formal way to describe and analyze the time complexity of recursive algorithms. They help in understanding the growth rate of the algorithm as the input size increases, enabling us to evaluate the efficiency and scalability of the algorithm.