This study addresses the numerical solution of a nonlocal boundary-value issue for a two-dimensional pseudoparabolic equation that arises in a variety of physical events. For the solution of this problem, a three-layer alternating direction implicit approach is examined. Peaceman-ADI Rachford's approach for the 2D parabolic equation is generalised in this method. The suggested method's stability is demonstrated in the specific norm. To demonstrate its stability, we study the algebraic eigenvalue problem using nonsymmetric matrices.
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