A Designed ADI Software for Solving Poisson’s Equation

P-adi Constraint Solving

A Matched Alternating Direction Implicit (ADI) Method for Solving the Heat Equation with Interfaces

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due to its unconditional stability and high efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different mater...

Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation

The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and s...

Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation

For large scale problems, an effective approach for solving the algebraic Lyapunov equation consists of projecting the problem onto a significantly smaller space and then solving the reduced order matrix equation. Although Krylov subspaces have been used for long time, only more recent developments have shown that rational Krylov subspaces can be a competitive alternative to the classical and v...

A method for solving first order fuzzy differential equation