in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...

This letter simplifies and analyze existing state evolution recursions for conjugate gradient. The proposed simplification reduces the complexity solving from cubic order to square in total number of iterations. simplified are still catastrophically sensitive numerical errors, so that arbitrary-precision arithmetic is used accurate evaluation recursions.

Abstract Terminal value problems of fractional linear systems with non-homegenous terms are investigated in this paper for the first time. They equivalent to a second kind weakly singular Volterra–Fredholm integral system. Picard’s method is used obtain closed form solution. The exact solution checked satisfy terminal problem. Numerical solutions provided comparison truncated ones.

The paper presentes a numerically stable and general algorithm for identification and realization of a complete dynamic linear state space model, including the system order, for combined deterministic and stochastic systems from time series. A special property of this algorithm is that the innovations covariance matrix and the Markov parameters for the stochastic sub-system are determined direc...