Simpson’s Rule in EXCEL

Introduction

Simpson's Rule is a well-known technique that works wonders for solving complicated mathematical integration equations. The lengthy numerical equation will take a lot of user time and effort if solved manually, increasing the probability of incorrect results. We have a plethora of effective techniques, such as the trapezoid rule and Gaussian integration methods, for tackling complex problems in Excel.

Problem Statement

Suppose we have to solve the numerical integration equation $\mathrm{N\:=\:\int_{1}^{3}\:exp\:(m^{3})\:dm}$ through Simpson’s Rule.

Explanation

Step 1

Users need to enter the text and values in the range A3:B6. Here the Bottom and Top values represent the upper and lower limit of the integration and t denotes the number of strips.

Step 2

Enter the formula “=(B4-B3))/B5” in the B6 cell and press the “Enter” tab to obtain the value.

Step 3

Write the starting value of F3 and G3 cells. Enter the formula “=B3” and “=EXP(B3^3)” in the F3 and G3 cells as highlighted in below image −

Step 4

Enter the second value of the m and n variables. Write the formula “=F3+B6” in the F4 cell that represents the value of m2 and then press the “Enter” tab.

Step 5

Now, write the formula “=EXP(F4^3)” in the G4 cell as given below −

And then press the “Enter” tab.

Step 6

Then copy the similar formulas for the F and G columns and drop down to the G11 cell as given below −

Step 7

You must give the heading “Simpson” in the H2 cell. Write the formula “=(B6/3)*(G3+4*G4+G5)” in the H3 cell and press “Enter” to get the result.

Step 8

Evaluate the same formula for a few cells. Users need to change the cell values except for the delta cell reference. Consider the below screenshot for your reference.

Therefore, the results are displayed in the H column.

Conclusion

We can conclude that one effective method for solving numerical integration problems is Simpson's Rule. To achieve an accurate answer, users must carefully enter each formula as shown in the given example otherwise, errors may arise.