The complementary error matrix function and its role solving coupled diffusion mathematical models

In this paper, the error function and the complementary error function of a matrix are introduced. Basic properties of these matrix functions are studied and applied to the inverse Laplace transform of a matrix function and to solve coupled diffusion models in a semi-infinite medium.

[1]  Lucas Jódar,et al.  Analytic numerical solution of coupled semi-infinite diffusion problems☆ , 1995 .

[2]  Kennet Axelsson,et al.  UNCOUPLING OF COUPLED FLOWS IN SOIL-A FINITE ELEMENT METHOD , 1995 .

[3]  J. Stoer,et al.  Introduction to Numerical Analysis , 2002 .

[4]  Gene H. Golub,et al.  Matrix computations , 1983 .

[5]  R. F. Rinehart.  The derivative of a matric function , 1956 .

[6]  James K. Mitchell,et al.  Coupled fluid, electrical and chemical flows in soil , 1993 .

[7]  J. Dieudonne.  Foundations of Modern Analysis , 1969 .

[8]  J. Clunie.  Analytic Functions , 1962, Nature.

[9]  Hirofumi Morimoto,et al.  Stability in the wave equation coupled with heat flow , 1962 .

[10]  Lokenath Debnath.  On certain integral transforms and their applications , 1964 .

[11]  Edwin Hewitt,et al.  Foundations of Modern Analysis (vol. X of Pure and Applied Mathematics). , 1961 .

[12]  Inmaculada Higueras,et al.  Logarithmic Norms for Matrix Pencils , 1999, SIAM J. Matrix Anal. Appl..

[13]  Lucas Jódar,et al.  A matrix D'Alembert formula for coupled wave initial value problems , 1998 .

[14]  Herschel Rabitz,et al.  A GENERAL LUMPING ANALYSIS OF A REACTION SYSTEM COUPLED WITH DIFFUSION , 1991 .

[15]  T. M. Flett.  Differential Analysis: Notes , 1980 .

[16]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[17]  Michael Mascagni,et al.  An initial-boundary value problem of physiological significance for equations of nerve conduction , 1989 .