- #1

- 50

- 0

2. What are the solution methods (theoretical and numerical) for solving a system of simultaneous non-linear equations.

- Thread starter JulieK
- Start date

- #1

- 50

- 0

2. What are the solution methods (theoretical and numerical) for solving a system of simultaneous non-linear equations.

- #2

WWGD

Science Advisor

Gold Member

2019 Award

- 5,415

- 3,501

- #3

Stephen Tashi

Science Advisor

- 7,480

- 1,416

Are you using "non-linear" to mean equations involving polynomials? Or are you asking about any kind of non-linear equation?2. What are the solution methods (theoretical and numerical) for solving a system of simultaneous non-linear equations.

- #4

- 50

- 0

Any kind not only polynomials.

- #5

Stephen Tashi

Science Advisor

- 7,480

- 1,416

For such a large class of equations, there is no general test like the determinant test.Any kind not only polynomials.

- #6

Chestermiller

Mentor

- 20,623

- 4,452

For numerically solving sets of coupled non-linear algebraic equations, Newton-Raphson (and modifications thereof) are often very effective.What are the solution methods (theoretical and numerical) for solving a system of simultaneous non-linear equations.

Chet

- #7

- 50

- 0

- #8

Chestermiller

Mentor

- 20,623

- 4,452

If it is a physical problem, and the model equations are formulated correctly, then there should exist a solution. As far as obtaining the required solution to a set of non-linear algebraic equations for a physical problem, there is no set recipe. The trick is to get an initial guess that is close enough to the required solution for Newton-Raphson (or other method, such as successive substitution) to converge. The method used for getting a good initial guess depends on the specific problem. But it is mostly a matter of playing with the equations, and having some experience. Do you have a specific problem in mind that you would like to lay on the table?

Chet