The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

This paper is concerned with the solution of systems of linear equations ANx = b, where fANg N2N denotes a sequence of positive deenite Hermitian ill{conditioned Toeplitz matrices arising from a (real{valued) nonnegative generating function f 2 C2 with zeros. We construct positive deenite Hermitian preconditioners MN such that the eigenvalues of M ?1 N AN are clustered at 1 and the correspondin...

We consider a class of PT -symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of PT -invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a line...

Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a series of linear system of equations (Jacobian system). In this article, we adaptively define the tolerance of the Jacobian systems. Numerical experiment show...

We present an algorithm for solving a linear system in a symmetric M-matrix. In particular, for n × n symmetric M-matrix M , we show how to find a diagonal matrix D such that DMD is diagonallydominant. To compute D, the algorithm must solve O (log n) linear systems in diagonally-dominant matrices. If we solve these diagonallydominant systems approximately using the Spielman-Teng nearly-linear t...

In this paper, a complete non-linear symmetric oscillator model using the Hamiltonian approach has been developed and used to describe cardiovascular conduction process’s dynamics, as signal generated from muscle is non-deterministic random. Electrocardiogram (ECG) significant factor in system most of medical diagnoses can be well understood by observing ECG signal’s amplitude. A proposed study...

Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the ra...