How to perform multivariable numerical integration?

In summary, the speaker is struggling with numerically integrating a multivariable function and is unsure of how to do so. They mention being familiar with integrating single variable functions but have no knowledge of how to do this for multivariable functions. They ask for advice on how to use the trapezoidal rule for integration and mention having two books on numerical methods but finding no information on this topic. However, they later realize their mistake and figure out the solution. They also suggest using H. Engels' "Numerical Quadrature and Cubature" for integrating with 2 variables and Monte Carlo integration for multiple variables.
  • #1
Topher925
1,566
7
I've got a problem where I need to numerically integrate a multivariable function but I'm not sure how to do this. I'm more than familiar with how to numerically integrate a single variable function numerically but I have no clue how to do this for a multivariable function. For example let's say I have the function

P = (x2 + 4xy)

and I need to integrate this numerically between some definite closed bounds of x, y, and z using the trapezoidal rule. How would one go about doing this? Would I simply perform the integration on each variable and then plug that solution into the respective variable for that function for each integral I evaluate? I have two books on numerical methods and none of them mention anything about doing this. Is it even possible?
 
Physics news on Phys.org
  • #2
Nevermind, I figured it out. Just had a bit of a stupid moment.
 
  • #3
For the record: with 2 variables, see H. Engels, "Numerical Quadrature and Cubature", Academic, 1980. For many variables, use Monte Carlo integration.
 

Related to How to perform multivariable numerical integration?

1. How do I choose the appropriate method for multivariable numerical integration?

Choosing the appropriate method for multivariable numerical integration depends on the specific problem at hand. Some common methods include Simpson's rule, trapezoidal rule, and Monte Carlo integration. Factors to consider when selecting a method include the number of dimensions, smoothness of the function, and desired accuracy.

2. What is the difference between single-variable and multivariable numerical integration?

In single-variable numerical integration, the goal is to approximate the definite integral of a function with respect to a single variable. In multivariable numerical integration, the goal is to approximate the definite integral of a function with respect to multiple variables. This requires the use of more advanced methods and techniques.

3. Can I use software or programming languages to perform multivariable numerical integration?

Yes, there are many software programs and programming languages that have built-in functions or libraries for performing multivariable numerical integration. Some popular options include MATLAB, Python, and R. These tools can make the process faster and more accurate than performing the calculations by hand.

4. How can I check the accuracy of my multivariable numerical integration results?

One way to check the accuracy of your results is to compare them to the analytical solution if one is available. Another method is to vary the number of integration points or use a different method and compare the results. Additionally, you can use convergence tests to determine the rate at which the approximation is approaching the true solution.

5. What are some common challenges in performing multivariable numerical integration?

Some common challenges in multivariable numerical integration include dealing with high-dimensional functions, finding appropriate weights for the integration points, and handling singularities or discontinuities in the function. It is also important to carefully consider the choice of method and the accuracy requirements for the specific problem at hand.

Similar threads

MHB Multivariate gaussian integral
    • Calculus
Replies
1
Views
1K
I Second derivative of chained function
    • Calculus
Replies
14
Views
1K
A Need help with an integral -- How to integrate velocity squared?
    • Calculus
Replies
3
Views
1K
I Integration with different infinitesimal intervals
    • Calculus
Replies
31
Views
1K
I Decomposing a Function for Numerical Integration
    • Calculus
Replies
1
Views
1K
A Memory issues in numerical integration of oscillatory function
    • General Math
Replies
3
Views
535
I Multivariable fundamental calculus theorem in Wald
    • Calculus
Replies
2
Views
1K
I Is there such a thing as an antiderivative of a multivariable function?
    • Calculus
Replies
9
Views
3K
B Explain Integration to me, please
    • Calculus
Replies
5
Views
2K
I Gaussian Quadrature on a Repeated Integral
    • Calculus
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top