Singular point affected by parameters of ODEs

In summary, the conversation discusses solving a set of boundary value ODEs numerically with ten parameters, and finding that the solution may be singular at an endpoint. The question is raised about determining the composition of parameters that affect the property of the equations and if there are existing theories for this. Suggestions are made to use methods such as singular perturbation or numerical techniques, but the process of finding the composition of parameters is still uncertain.
  • #1
SHmech
3
0

Homework Statement



I'm trying to solve a set of boundary value ODEs numerically, which contains about ten parameters. And i found that with some values of parameters, the solution may be singular at an endpoint(Maple says "system is singular at the righthand endpoint").

So i guess there may be a composition of the parameters which affects the property of the set of ODEs. The questions is, how can i find out the composition and in which way does the composition affects the property of the equations? Are there some theories about this?

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
I guess i should use some methods like singular perturbation or some numerical techniques to solve the equations. But i'm not sure how to find out the composition of parameters which affects the property of the equations.
 

1. What is a singular point in an ODE?

A singular point in an ODE (ordinary differential equation) is a point where the solution of the equation becomes undefined or infinite. This means that the behavior of the solution at this point is different from the rest of the solution.

2. How do parameters affect the singular point in an ODE?

The parameters in an ODE can affect the location, nature, and stability of the singular point. Changing the values of the parameters can cause the singular point to shift, disappear, or become stable or unstable.

3. What is the significance of studying singular points affected by parameters in an ODE?

Studying the singular points affected by parameters in an ODE can help us understand the behavior and stability of the overall solution. It can also provide insights into the underlying dynamics of the system and how different parameters can impact the system's behavior.

4. How can we analyze the effects of parameters on singular points in an ODE?

There are various analytical and numerical methods for analyzing the effects of parameters on singular points in an ODE. These include phase plane analysis, perturbation methods, and numerical simulations using software such as MATLAB or Mathematica.

5. Can the parameters in an ODE be adjusted to control or avoid singular points?

In some cases, adjusting the parameters in an ODE can help control or avoid singular points. However, this depends on the specific system and cannot be generalized. In other cases, singular points may be unavoidable and can provide valuable information about the behavior of the system.

Similar threads

Perturbation Methods: Asymptotic Matching Question
    • Calculus and Beyond Homework Help
Replies
2
Views
709
Solving a second order ODE using reduction of order
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Identifying Types of Singularity in Differential Equations
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Show Regular Homotopy thru curve and its arclength parameters
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Partial Differential Equation with variable coefficients
    • Calculus and Beyond Homework Help
Replies
6
Views
2K
Solving Systems of Inhomogeneous Linear ODEs: A Step-by-Step Guide
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
How Do Matrix ODEs Relate to Determinants and Traces?
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
    • Calculus and Beyond Homework Help
Replies
2
Views
379
Finding the homogenous solution of Var.Coeff. 2nd Order ODE
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Boundary Value ODE: Eigenvalues & Functions
    • Calculus and Beyond Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top