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In this paper, an approximate method is presented for computing exponentialof tridiagonal Toeplitz matrices. The method is based on approximating elementsof the exponential matrix with modified Bessel functions of the first kind incertain values and accordingly the exponential matrix is decomposed assubtraction of a symmetric Toeplitz and a persymmetric Hankel matrix with noneed for the matrix multiplication. Also, the matrix is approximated by a bandmatrix and an error analysis is provided to validate the method.Generalizations for finding exponential of block Toeplitz tridiagonal matricesand some other related matrix functions are derived. Applications of the newidea for solving one and two dimensions heat equations are presented and thestability of resulting schemes is investigated. Numerical illustrations showthe efficiency of the new methods.

Exponential of tridiagonal Toeplitz matrices: applications and generalization