# SIMPSONS RULES

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Category: Education

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## Presentation Transcript

### NUMERICAL INTEGRATION :

NUMERICAL INTEGRATION SIMPSON’S RULES

### SIMPSON’S RULES :

SIMPSON’S RULES THE COMPOSITE NEWTON-COTES FORMULAS BASED ON QUADRATIC & CUBIC INTERPOLATING POLYNOMIALS ARE KNOWN AS SIMPSON’S RULES. THE FIRST, BASED ON A QUADRATIC, IS KNOWN AS SIMPSON’S 1/3 RULE. THE SECOND, BASED ON A CUBIC, IS KNOWN AS THE SIMPSON’S 3/8 RULE. THESE NAMES COME FROM THE COEFFICIENTS OF THE FORMULAS.

### SIMPSON’S 1/3 RULE :

SIMPSON’S 1/3 RULE THE SECOND-DEGREE NEWTON-COTES FORMULA INTEGRATES A QUADRATIC OVER TWO INTERVALS OF EQUAL WIDTH. THE INTERVALS ARE CALLED PANELS.

### SIMPSON’S 1/3 RULE :

SIMPSON’S 1/3 RULE FROM THESE FORMULAS, A COMPOSITE RULE IS APPLIED TO A SUBDIVISION OF THE INTERVAL OF INTEGRATION IN n NUMBER OF PANELS. THE n MUST BE AN EVEN INTEGER. WHERE a AND b ARE END POINTS.

### SIMPSON’S 3/8 RULE :

SIMPSON’S 3/8 RULE THE COMPOSITE RULE BASED ON FITTING FOUR POINTS WITH A CUBIC LEADS TO SIMPSON’S 3/8 RULE. THE n MUST BE DIVISIBLE BY 3.