Picard Iteration
Build an ODE solution by repeatedly integrating the previous approximation.
Free theory articleBuild an ODE solution by repeatedly integrating the previous approximation.
Concept & interpretation
For the initial value problem y' = ay, y(0) = 1, Picard iteration constructs an integral sequence of successive approximations. It builds an ODE solution by repeatedly integrating the previous approximation. The process generates the Taylor series for the exact solution.
Experiment
Use the Picard Iteration module to visualize successive integral iterates.
- Set Rate a to 1 and Time t to 1. Observe that for Iteration n = 2, the Approximation is 2.5 and ODE residual is -0.5.
- Change Iteration n to 6. Observe that the Approximation improves to ~7.355 and absolute error drops significantly.