Name of a type of differential equations

Click For Summary
SUMMARY

The discussion centers on Fredholm integral equations of the first kind, specifically focusing on the equations defined by the integrals ∫η(x)ω(x)=0 and ∫η'(x)ω(x)=0. The user, Kev, seeks references and assistance in solving these equations with a known function ω(x) and specified limits. The community confirms the classification of these equations and provides insights into their properties and solutions.

PREREQUISITES
  • Understanding of integral equations, specifically Fredholm integral equations.
  • Familiarity with the concept of functions and their derivatives.
  • Knowledge of mathematical analysis and calculus.
  • Ability to work with known functions and limits in integrals.
NEXT STEPS
  • Research the properties and solutions of Fredholm integral equations of the first kind.
  • Explore numerical methods for solving integral equations.
  • Study specific examples of applications of Fredholm integral equations in physics and engineering.
  • Learn about software tools for solving integral equations, such as MATLAB or Mathematica.
USEFUL FOR

Mathematicians, physicists, and engineers interested in solving integral equations, particularly those working with Fredholm integral equations in applied contexts.

kevchang
Messages
3
Reaction score
0
Dear all,

I am interested in solving the following type of system of differential equations for η(x):

(1) ∫η(x)ω(x)=0
(2) ∫η'(x)ω(x)=0

for known ω(x), and known limits of the integral. Does this type of equations have a name? Can someone help me to find some reference? Thanks a ton!

Cheers,
Kev
 
Physics news on Phys.org
These are Fredholm integral equations of the first kind.
 

Similar threads

Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Differential equation using power series method
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Is there a name for this sort of differential equation?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad General solution vs particular solution
  • · Replies 52 ·
2
Replies
52
Views
9K
Graduate Differential equation and Appell polynomials
  • · Replies 1 ·
Replies
1
Views
4K
Graduate FEM basis polynomial order and the differential equation order
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Quick Change of Variables Question
  • · Replies 15 ·
Replies
15
Views
2K
MHB Solve Differential Eq: xe^-1/(k+e^-1) for x, k, t
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Solve the Partial differential equation ##U_{xy}=0##
  • · Replies 3 ·
Replies
3
Views
4K