Open AccessFourth-Order Approximation of the Fundamental Matrix of Linear System of Differential Equations
Author(s) -
anan hussein
Publication year - 1997
Publication title -
maǧallaẗ ǧāmiʿaẗ al-sulṭān qābūs li-l-ʿulūm/sultan qaboos university journal for science
Language(s) - English
Resource type - Journals
eISSN - 2414-536X
pISSN - 2308-3921
DOI - 10.24200/squjs.vol2iss0pp57-64
Subject(s) - matrix exponential , mathematics , boundary value problem , matrix (chemical analysis) , mathematical analysis , coefficient matrix , discretization , exponential integrator , differential equation , ordinary differential equation , differential algebraic equation , physics , eigenvalues and eigenvectors , quantum mechanics , composite material , materials science
A fourth-order approximation to the fundamental matrix of a system of linear differential equations is presented in closed form as a matrix exponential. The matrix exponential is then discretized over the interval of integration l‘adc approximation together with the method of scaling and squaning (Moler et at 1978) is used to evaluate the matrix exponential. This approach is suitable for solving both initial and boundary value problems with mixed boundary conditions. The approximating matrix can also be used as an integrating operator for methods which require information about the solution along the discretized subintervals. An example of a boundary value problem with mixed boundary condition is presented.