Abstract: This paper presents a modified formula for Simpson rule with third derivatives of endpoint and its truncation error.It also displays an analysis on convergence order of compound formula.Though compound modified formula for Simpson rule with endpoint derivatives just calculates a newly-added third derivative of the two endpoints for each time compared with compound Simpson formula calculation,there are 2 more ranks of the convergence order in this modified formula.Examples of numerical calculation have validated theoretical analysis.

Key words: numerical integration, Simpson formula, algebraic accuracy, truncation error, convergence order