This article introduces the matrix differential transform method (MDTM) to apply to matrix partial differential equations (MPDEs) and employs it for solving matrix Fisher equations, matrix Burgers equations and matrix KdV equations. We show how the MDTM applies to the linear part and nonlinear part of any MPDE and give various examples of MPDEs to illustrate the efficiency of the method. The results obtained are in excellent agreement with the exact solution and show that the proposed method is powerful, accurate, and easy.
Khader, M. M. and Borhanifar, A.
Implementation of the matrix differential transform method for obtaining an approximate solution of some nonlinear matrix evolution equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
2, Article 27.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/27