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Evolution operator approach for solving linear ordinary differential equations and computation of EXP (A)

Azzam, Abdelnasser
An Evolution Operator Approach which were developed to solve nonlinear O.D.E. systems, X=f(x), X(0)=£, is discussed for the linear systems X=AX where A is nxn symmetric matrix. In this approach, each component of the solution vector is represented as an action of evolution operator, exp(itL), on xj and then approximated by method of Moment using [N+1,N] Pade’ approximation. In applications, the most important part of this method is the computation of dynamical and spectral coefficients [6]. The recursive formulation of the dynamical coefficients are used to achieve the analytic formulation of spectral coefficients for the case N=l. The exponential matrix, eA, for symmetric matrix A, is computed approximately using the numerical solution of the initial value problem with the initial conditions X(0) = e , j=l,2, ...,n. Also some modifications are applied to improve die numerical results.