The Picard Iteration

Picard iteration is a method for solving differential equations by gradually approaching a solution. Starting with an initial guess, it creates a sequence of improved approximations by repeatedly applying an integral formula derived from the differential equation. Each step refines the previous estimate, and under suitable conditions, this process converges to the exact solution. Essentially, it’s an iterative process that refines an initial estimate until it closely matches the true behavior described by the differential equation, providing a practical way to approximate solutions when exact formulas are difficult to find.