Nonlinear system of algebraic equations

In summary, the conversation is about finding a good method to solve a nonlinear system of algebraic equations in order to numerically solve a PDE. The suggested method is to use Newton's Method, which involves calculating partial derivatives.
  • #1
cesarmv
2
0
Hello,

It's my first topic here. :)
In order to solve a PDE numerically, I have reached in a nonlinear system of algebraic equations. Does anyone here know a good method to solve it numerically?

It seems like this:

xij (t+dt) is proportional to xi,j+1(t), xij2(t), xi,j-12(t), xi-1,j(t), xi+1,j(t), etc..

where i and j are 'coordinates' of a 2D grid.

Thank you so much in advance.



César.
 
Technology news on Phys.org
  • #3
Ok, I'll take a look, thanks!
 

1. What is a nonlinear system of algebraic equations?

A nonlinear system of algebraic equations is a set of equations where the unknown variables appear as exponents or in trigonometric functions, making it difficult to solve using traditional methods. These systems often have multiple solutions or no solutions at all.

2. How is a nonlinear system of equations different from a linear system?

A linear system of equations has only first-order variables, meaning they are not raised to any power or found in trigonometric functions. This allows for a unique solution to be found using methods such as elimination or substitution. Nonlinear systems, on the other hand, have higher-order variables and may require more advanced techniques to solve.

3. What are some common techniques for solving nonlinear systems of equations?

Some common techniques used to solve nonlinear systems of equations include substitution, elimination, graphing, and iteration. These methods may require multiple steps and iterations to find a solution, and the choice of technique may depend on the specific system of equations.

4. Can a nonlinear system of equations have more than one solution?

Yes, a nonlinear system of equations can have multiple solutions, as opposed to a linear system which typically has a unique solution. This is due to the complex nature of nonlinear equations, which may have multiple points of intersection or no intersection at all.

5. How can solving a nonlinear system of equations be useful in real-world applications?

Nonlinear systems of equations are often used in scientific and engineering fields to model complex systems and phenomena. By solving these equations, we can gain a better understanding of real-world scenarios and make predictions or optimizations based on the solutions.

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