The stability of certain partial difference equations
This paper is concerned with the linear delay partial difference equation u(i,j + 1) = a(i,j)u(i + 1,j) + b(i,j)u(i,j) + p(i,j)u(i - sigma, j - tau), where sigma and tau are positive integers, a(i, j), b(i, j), p(i,j) are real sequences defined on i greater than or equal to sigma, j greater than or equal to tau. Sufficient conditions for this equation to be stable are derived. Stability of certain nonlinear partial difference equations is studied also. (C) 2001 Elsevier Science Ltd. All rights reserved.
stability delay partial difference equation liapunov function