Non-linear differential equation

In summary, the speaker is writing a function for a non-linear differential equation with Robin BC in their numerical analysis class. They want to find a program that can solve example equations numerically to ensure their function is working correctly, but have had trouble finding one that works on a Mac and can handle Robin BC. They mention finding a solution to the equation themselves, but are still interested in a reliable program for future use.
  • #1
Heimisson
44
0
Hi I'm writing a function (matlab) in my numerical analysis class that descripes in a certain way a non-linear differential equations with Robin BC that I will then feed to a program that uses finite difference method to solve it. It seems to work but I wanted to look for a site or program that could solve some example equations numerically so I can be sure that it's working correctly. WolframAlpha doesn't seem to handle Robin BC and by googling I only found programs that don't work on mac.

thanks
 
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  • #2
Never mind I found a solution to the equation, although a trustworthy program would be useful.
 

1. What is a non-linear differential equation?

A non-linear differential equation is a mathematical equation that involves an unknown function and its derivatives, where the function is not directly proportional to its derivatives. In other words, the function and its derivatives are not related in a simple, linear way.

2. How is a non-linear differential equation different from a linear one?

A linear differential equation involves a function and its derivatives in a linear relationship, meaning that the function and its derivatives can be written as a linear combination of each other. A non-linear differential equation does not have this property and often involves powers, products, or trigonometric functions of the function and its derivatives.

3. What are some real-life applications of non-linear differential equations?

Non-linear differential equations are used to model many natural phenomena, such as population growth, chemical reactions, and fluid dynamics. They are also used in engineering, economics, and neuroscience to describe complex systems and their behaviors.

4. How are non-linear differential equations solved?

Unlike linear differential equations, there is no general method for solving non-linear differential equations. In most cases, numerical methods or approximations are used to find solutions. Some simpler non-linear differential equations can be solved analytically using techniques such as separation of variables or substitution.

5. What are some challenges in working with non-linear differential equations?

Non-linear differential equations can be difficult to solve and analyze compared to linear ones. They often have no closed-form solutions, making it necessary to use numerical methods or approximations. Non-linear equations can also exhibit chaotic behavior, where small changes in initial conditions can lead to drastically different solutions, adding to the complexity of working with them.

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