Butcher tableau is essentially a compact recipe card that defines a specific Runge-Kutta method for solving ordinary differential equations. It neatly organizes all the coefficients you need for the calculation into a single table.

Definition

A Butcher Table represents a Runge-Kutta method for solving ordinary differential equations . It encodes how to compute intermediate stages and combine them to advance the solution.

General Form

  • time increments for intermediate stages
  • coefficients for combining previous values in each stage
  • final weights for combining all values to get
  • intermediate slope evaluations