ADI Method for Pseudoparabolic Equation with Nonlocal Boundary Conditions

Abstract

This paper deals with the numerical solution of nonlocal boundary-value problem for two-dimensional pseudoparabolic equation which arise in many physical phenomena. A three-layer alternating direction implicit method is investigated for the solution of this problem. This method generalizes Peaceman–Rachford’s ADI method for the 2D parabolic equation. The stability of the proposed method is proved in the special norm. We investigate algebraic eigenvalue problem with nonsymmetric matrices to prove this stability. Numerical results are presented.

Keywords

• pseudoparabolic equation
• nonlocal conditions
• finite difference method
• ADI method
• eigenvalue problem for difference operator