STEPWISE STABILITY FOR THE HEAT EQUATION WITH A NONLOCAL CONSTRAINT

摘要

The authors prove the stepwise stability for a finite difference scheme for the heat equation with an integral constraint. The resulting matrix is nonsymmetric and does not have the usual band structure. The proof is based on the method of matrix analysis. The eigenvalues of several matrices are found explicitly or their location described precisely. This method relies upon the relationship of the characteristic polynomials of these matrices with orthogonal polynomials. [References: 34]