L-Stable Derivative-Free Error-Corrected Trapezoidal Rule for Burgers' Equation with Inconsistent Initial and Boundary Conditions

Abstract EN

We combine suitable arithmetic average approximations, with explicit backward Euler formula, and derive a third-order L-stable derivative-free error-corrected trapezoidal rule (LSDFECT).

Then, we apply LSDFECT rule to the linearized Burgers' equation with inconsistent initial and boundary conditions and test its stability and exactness.

We use Mathematica 7.0 for computation.