The Trajectory of a Solution to a Lorenz' Equation
The Modified Picard Method
 
(Power Series Method)
by
James Sochacki
Edgar G. Parker

An Expository Document on Using the Modified Picard Method to Solve Initial Value Ordinary Differential and Partial Differential Equations

Paper I - Implementing the Picard Method

Paper II - A-priori Error Estimates for Initial Value ODE's

Paper III - Properties of Polynomial Systems of ODE's

Paper IV - A Picard-McLaurin Theorem for Initial Value PDE's

Paper V - Neuron Application Using Parker Sochacki

Paper VI - Planetary Motion Application Using Parker Sochacki

Paper VII - Parallel Computing Using PSM

Paper IIX - Polynomial ODEs

Paper IX - Connections of PSM with Automatic Differentiation

Paper X - What Moves You: Using Legs for Vehicular Transportation

Paper XI - Delay Differential Equations

Paper XII - Boundary Value Problems

SEARCDE 2010           (conference)

AIMS 2012            (conference)

Taylor Center

Matlab Code that Solves General Quadratic IVODE's using PSM

Maple Code that Solves General Quadratic IVODE's using PSM

Maple Code that Solves General Polynomial IVODE's using Modified Picard

Matlab Code that Solves Newton's N-Body Problem using PSM