Fredholm Integral Equation Visualizer

Fredholm Integral Equation Visualizer

Interactive demonstration of 1st and 2nd kind Fredholm equations

Equation Type

First Kind Fredholm Equation:

∫_a^b K(x,s)φ(s) ds = f(x)

Second Kind Fredholm Equation:

φ(x) = f(x) + λ∫_a^b K(x,s)φ(s) ds

Interactive Solver

Kernel K(x,s): x·s sin(x+s) exp(-|x-s|)

λ (lambda):

f(x): x x² sin(x)

Solution plot will appear here

About Fredholm Equations

Fredholm integral equations appear in:

• Physics (potential theory)
• Image processing
• Finance (option pricing)
• Inverse problems

First kind are typically ill-posed, while second kind are usually well-posed.

This demo uses simple numerical approximation methods.