special forms of the fifth order kdv equation with new periodic and soliton solutions abstract in this paper we consider two special forms of the fifth order kdv equation fkdv that are of particular significance the lax and sawada koterra sk equations using a generalization of extended tanh method new periodic and solitons solutions for this equations are formally obtained

analytical solution for the time fractional telegraph equation by the method of separating variables in this paper a method of separating variables is effectively implemented for solving a time fractional telegraph equation tfte we discuss and derive the analytical solution of the tfte with three kinds of nonhomogeneous boundary conditions namely dirichlet neumann and robin boundary conditions

time fractional telegraph equations and telegraph processes with brownian time we study the fundamental solutions to time fractional telegraph equations of order 2 we are able to obtain the fourier transform of the solutions for any and to give a representation of their inverse in terms of stable densities for the special case 1 2 we can show that the fundamental solution is the distribution of a telegraph process with brownian time in a special case this becomes the density of the iterated brownian motion which is therefore the fundamental solution to a fractional diffusion equation of order 1 2 with respect to time

an approximate analytical solution of time fractional telegraph equation abstract in this article the powerful easy to use and effective approximate analytical mathematical tool like homotopy analysis method ham is used to solve the telegraph equation with fractional time derivative 1

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

the extended tanh method for new solitons solutions for many forms of the fifth order kdv equations abstract the extended tanh method is used to derive new solitons solutions for several forms of the fifth order nonlinear kdv equation the forms include the lax sawada kotera sk sawada kotera parker dye skpd kaup kupershmidt kk kaup kupershmidt parker dye kkpd and the ito equations the criteria established in a m wazwaz abundant solitons solutions for several forms of the fifth order kdv equation by using the tanh method appl math comput in press doi 10 1016 j amc 2006 02 047 to build up reliable relations between the parameters of the equation are confirmed by using this new approach entirely new bell shaped solitons are determined

solution of a duffing harmonic oscillator by the method of harmonic balance abstract the first order harmonic balance method via first fourier coefficient is used to construct an approximate frequency amplitude relation for a duffing harmonic oscillator this relation is in agreement with the result obtained by the ritz procedure

directed polymers in a random medium 1 d expansion and the n tree approximation the authors develop a method which allows one to obtain 1 d expansions for the problem of directed polymers in a random medium using this method they expand thermal properties such as the free energy the specific heat the overlaps and the fluctuations of the transverse displacement their results are consistent with the existence of a finite upper critical dimension above which the low temperature phase is mean field like i e characterised by a broad distribution of overlaps broken replica symmetry and transverse fluctuations which scale as the length of the polymer

a diffusion wave equation with two fractional derivatives of different order we analyse a diffusion wave equation with two fractional derivatives of different order on bounded and unbounded spatial domains thus our model represents a generalized telegraph equation solutions to signalling and cauchy problems in terms of a series and integral representation are given classical wave and heat conduction equations are obtained as limiting cases

universal scaling law for the largest lyapunov exponent in coupled map lattices coupled map lattices cmls 1 as discrete analogs tocoupled oscillators and partial differential equations havein recent years become the model of choice for developingintuitions and concepts in the study of spatiotemporalchaotic systems among the variety of quantities appliedto characterize the dynamics of a cml the spectrum oflyapunov exponents stands out for its ease of numericalevaluation and for the wealth of information that derivesfrom it for example from pesin s formula 2 thesum of all positive lyapunov exponents provides anestimate of the kolmogorov sinai entropy meanwhile one obtains the information dimension of the chaoticattractor by employing the kaplan yorke conjecture 3 moreover the largest lyapunov exponent lle denotedhenceforth by l quanti es the sensitive dependence oninitial conditions a hallmark of chaos 4 by yieldingthe rate of exponential divergence of two typical nearbytrajectories in this letter we focus on the scaling behavior of lnear certain limiting situations consider a diffusivelycoupled map lattice of the form

lyapunov exponents of large sparse random matrices and the problem of directed polymers with complex random weights we present results on two different problems the lyapunov exponent of large sparse random matrices and the problem of polymers on a cayley tree with random complex weights we give an analytic expression for the largest lyapunov exponent of products of random sparse matrices with random elements located at random positions in the matrix this expression is obtained through an analogy with the problem of random directed polymers on a cayley tree i e in the mean field limit which itself can be solved using its relationship with random energy models rem and grem for the random polymer problem with complex weights we find that in addition to the high and the low temperature phases which were already known in the case of positive weights the mean field theory predicts a new phase phase iii which is dominated by interference effects

scaling law and asymptotic distribution of lyapunov exponents in conservative dynamical systems with many degrees of freedom the authors study by numerical means the infinite product of 2n 2n conservative random matrices which mimics the chaotic behaviour of hamiltonian systems with n 1 degrees of freedom made of weakly nearest neighbour coupled oscillators the maximum lyapunov exponent lambda 1 exhibits a power law behaviour as a function of the coupling constant epsilon lambda 1 approximately epsilon beta with either beta 1 2 or beta 2 3 depending on the probability distribution of the matrix elements these power laws do not depend on n and moreover increasing n lambda 1 rapidly tends to an asymptotic value lambda 1 which only depends on epsilon and on the kind of probability distribution chosen for building up the matrices they also compute the spectrum of the lyapunov exponents and show that is has a thermodynamic limit of large n this suggests the existence of a kolmogorov entropy per degree of freedom proportional to lambda 1

the variational iteration method for rational solutions for kdv k 2 2 burgers and cubic boussinesq equations in this work the reliable variational iteration method is used to determine rational solutions for the kdv the k 2 2 the burgers and the cubic boussinesq equations the study highlights the efficiency of the method and its dependence on the lagrange multiplier rational solutions are obtained directly in a straightforward manner

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

vanishing gaps in 1d bandstructures the criterion for vanishing or zero energy gaps in the spectrum of 1d electronic bandstructures is obtained from perturbation theory it is in agreement with examples of periodic potentials which never exhibit zero gaps as well as with those which may including certain smooth periodic potentials the results have relevance to recent work in the field of semiconductor layered heterostructures or superlattices the analysis should also have implications for other problems that involve hill s determinant

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

variational approach to the lane emden equation by the semi inverse method a variational principle is obtained for the lane emden equation which gives much numerical convenience when applying finite element methods or ritz method

a perturbation technique that works even when the non linearity is not small abstract we extend the lindstedt poincare small non linearity based perturbation scheme to strongly non linear systems the extended technique starts from a physically non existent neighboring linear system this system is created by adding an optimal linear spring term to the system side of each linear differential equation starting at the zeroth level and balancing that term by adding an equal one to the forcing side one level down unlike the ritz method which also works for strongly non linear systems results can be obtained beyond the first level without resorting to numerical techniques thus the extended method keeps the intuition guiding straightforwardness of the perturbation method while giving accurate beyond first level hand derivable numerical results examples are presented for free vibrations with cubic and antisymmetric quadratic non linearities and for harmonic solutions of the undamped duffing equation the forms of the solutions allow the regions of validity of the expansions to be estimated an internal method of estimating accuracy of the perturbation solutions is developed and checked with the free vibration examples the exact solutions of which are available this internal method is then used to estimate the accuracy of the new solutions to the duffing equation these new duffing equation solutions give accurate results in all regions where stable harmonic solutions are known to exist in particular they give accurate results at and near the vertical tangent to the resonance curve a region where hayashi s amplitude expansion based perturbation solution necessarily breaks down

the variational iteration method combined with improved generalized tanh coth method applied to sawada kotera equation abstract we obtain new exact solutions to generalized sawada kotera equation using the variational iteration method combined with the improved generalized tanh coth method we construct new traveling wave solutions for the standard sawada kotera equation and by means of scaling we obtain new solutions to general sawada kotera equation periodic and soliton solutions are formally derived for both models

scaling law for the maximum lyapunov characteristic exponent of infinite product of random matrices the authors present a simple derivation for the scaling behaviour of the maximum lyapunov characteristic exponent lambda of infinite product of symplectic random matrices the considered random matrices depend on a parameter epsilon and lambda 0 for epsilon 0 they obtain lambda varies as epsilon beta with either beta 1 2 or beta 2 3 depending on the probability distribution of the matrix elements the results are in agreement with a previous numerical simulation

chirality of wavefunctions for three coalescing levels the analytic structure in the vicinity of three coalescing eigenvalues ep3 of a matrix problem is investigated it is argued that the three eigenfunctions also coalescing at the ep3 invoke a true chiral behaviour in the vicinity of the ep3 and that they can be related to a three dimensional helix the orientation of the helix depends on the distribution of the widths of the three levels in the vicinity of the ep3

fractional diffusion equation on fractals one dimensional case and asymptotic behaviour a fractional differential equation is studied and its application for describing diffusion on random fractal structures is considered it represents the simplest generalization of the fractional diffusion equation valid in euclidean systems the solution of the fractional equation in one dimension is discussed and compared with exact results for the fractional brownian motion and the one dimensional version of the standard diffusion equation on fractals in higher dimensions it correctly describes the asymptotic scaling behaviour of the probability density function on random fractals as obtained recently by using scaling arguments and exact enumeration calculations for the infinite percolation cluster at criticality

the generalized tanh coth method to special types of the fifth order kdv equation abstract in this paper we use a generalization of the well known tanh coth method to obtain new periodic and soliton solutions for several forms of the fifth order kdv equation fkdv three special cases that we consider here are the caudrey dodd gibbon cdg the generalized kaup kupershmidt gkk and the generalized ito equations new traveling wave solutions which include periodic and soliton solutions for three cases are formally derived

n tree approximation for the largest lyapunov exponent of a coupled map lattice the n tree approximation scheme introduced in the context of random directed polymers is applied here to the computation of the maximum lyapunov exponent in a coupled map lattice we discuss both an exact implementation for small tree depth n and a numerical implementation for larger n we find that the phase transition predicted by the mean field approach shifts towards larger values of the coupling parameter when the depth n is increased we conjecture that the transition eventually disappears

an analytic estimate of the maximum lyapunov exponent in products of tridiagonal random matrices in this work we present a theoretical and numerical study of the behaviour of the maximum lyapunov exponent in products of random tridiagonal matrices in the limit of small coupling and small fluctuations such a problem is directly motivated by the investigation of coupled map lattices in a regime where the chaotic properties are quite robust and yet a complete understanding has still not been reached we derive some approximate analytic expressions by introducing a suitable continuous time formulation of the evolution equation as a first result we show that the perturbation of the lyapunov exponent due to the coupling depends only on a single scaling parameter which in the case of strictly positive multipliers is the ratio of the coupling strength with the variance of local multipliers an explicit expression for the lyapunov exponent is obtained by mapping the original problem onto a chain of nonlinear langevin equations which are eventually reduced to a single stochastic equation the probability distribution of this dynamical equation provides an excellent description for the behaviour of the lyapunov exponent finally multipliers with random signs are also considered finding that the lyapunov exponent again depends on a single scaling parameter which however has a different expression

the optical singularities of birefringent dichroic chiral crystals using a new formalism involving projection from the sphere of directions to the stereographic plane and associated complex variables explicit formulae are obtained for the two refractive indices and polarizations in optically anisotropic crystals that are both dichroic absorbing and chiral optically active this enables three types of polarization singularity to be classified and explored singular axes which are degeneracies where the two refractive indices are equal and which for a transparent non chiral crystal condense pairwise onto the optic axes c points where the polarization is purely circular right or left handed with topological index 1 or and whose positions are independent of the chirality and l lines where the polarization is purely linear dividing direction space into regions with right and left handedness a local model captures essential features of the general theory interference figures generated by slabs of crystal viewed directly or through a polarizer and or analyser enable the singularities to be displayed directly

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method

a second order crank nicolson scheme for fractional cattaneo equation based on new fractional derivative abstract recently caputo and fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales in this article a crank nicolson finite difference scheme to solve fractional cattaneo equation based on the new fractional derivative is introduced and analyzed some a priori estimates of discrete l l2 errors with optimal order of convergence rate o 2 h 2 are established on uniform partition moreover the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis

the cole hopf transformation and improved tanh coth method applied to new integrable system kdv6 abstract in this paper we study a new coupled system kdv6 from the point of view of constructing exact solutions for it by using the cole hopf transformation and one improved tanh coth method traveling wave solution which includes periodic and soliton solutions are formally derived

computing exact solutions for some fifth kdv equations with forcing term abstract in this paper the extended tanh method is used to construct generalized soliton solutions periodic solutions and rational solutions for the sawada kotera and lax equations with forcing term

analytic and approximate solutions of the space and time fractional telegraph equations the adomian decomposition method is used to obtain analytic and approximate solutions of the space and time fractional telegraph equations the space and time fractional derivatives are considered in the caputo sense the analytic solutions are calculated in the form of series with easily computable terms some examples are given the results reveal that the adomian method is very effective and convenient

scaling law for the maximal lyapunov exponent the authors study the scaling law for epsilon to 0 of the maximal lyapunov exponent for coupled chaotic map lattices and for products of random jacobi matrices to this purpose they develop approximate analytical treatments of the random matrix problem inspired by the theory of directed polymers in a random medium a type of mean field method and a tree approximation which introduces correlations the theoretical results suggest a leading mod log epsilon mod 1 increase in the maximal lyapunov exponent near epsilon 0 which is confirmed by numerical simulations also for coupled map lattices a dynamical mechanism responsible for this behaviour is investigated for a 2 2 random matrix model the theory also predicts a phase transition at a critical value of the coupling epsilon e which is not observed in numerical simulations and might be an artifact of the approximation

on the variational iteration method and other iterative techniques for nonlinear differential equations abstract a variety of iterative methods for the solution of initial and or boundary value problems in ordinary and partial differential equations is presented these iterative procedures provide the solution or an approximation to it as a sequence of iterates for initial value problems it is shown that these iterative procedures can be written in either an integral or differential form the integral form is governed by a volterra integral equation whereas the differential one can be obtained from the volterra representation by simply differentiation it is also shown that integration by parts variation of parameters adjoint operators green s functions and the method of weighted residuals provide the same volterra integral equation and that this equation in turn can be written as that of the variational iteration method it is therefore shown that the variational iteration method is nothing else by the picard lindelof theory for initial value problems in ordinary differential equations and banach s fixed point theory for initial value problems in partial differential equations and the convergence of these iterative procedures is ensured provided that the resulting mapping is lipschitz continuous and contractive it is also shown that some of the iterative methods for initial value problems presented here are special cases of the bellman kalaba quasilinearization technique provided that the nonlinearities are differentiable with respect to the dependent variable and its derivatives but such a condition is not required by the techniques presented in this paper for boundary value problems it is shown that one may use the iterative procedures developed for initial value problems but the resulting iterates may not satisfy the boundary conditions and two new iterative methods governed by fredholm integral equations are proposed it is shown that the resulting iterates satisfy the boundary conditions if the first one does so the iterative integral formulation presented here is applied to ten nonlinear oscillators with odd nonlinearities and it is shown that its results coincide with those of differential two and three level iterative techniques harmonic balance procedures and standard and modified linstedt poincare techniques the method is also applied to two boundary value problems

construction of n soliton solutions to 2 1 dimensional konopelchenko dubrovsky kd equations abstract we make use of hirota s bilinear approach to find one two three four and in general n soliton solutions to 2 1 dimensional konopelchenko dubrobsky kd equations

computing exact solutions to a generalized lax seventh order forced kdv equation kdv7 abstract in this paper the cole hopf transform is used to construct exact solutions to a generalization of both the seventh order lax kdv equation lax kdv7 and the seventh order sawada kotera ito kdv equation sawada kotera ito kdv7 with forcing term

on the solutions of fractional swift hohenberg equation with dispersion in this article the approximate solutions of the non linear swift hohenberg equation with fractional time derivative in the presence of dispersive term have been obtained the fractional derivative is described in caputo sense time fractional nonlinear partial differential equations in the presence of dispersion and bifurcation parameters have been computed numerically to predict hydrodynamic fluctuations at convective instability for different particular cases and results are depicted through graphs

investigation of the properties of the period for the nonlinear oscillator x 1 x 2 x 0 abstract the mathematical properties of a nonlinear oscillator having the square of the angular frequency depend quadratically on the velocity is presented the major conclusion is that the exact period t a is well defined for all values of the amplitude where the initial conditions are taken to be x 0 a and x 0 0 an approximate expression is derived for t a

on the homotopy analysis method for nonlinear problems a powerful easy to use analytic tool for nonlinear problems in general namely the homotopy analysis method is further improved and systematically described through a typical nonlinear problem i e the algebraically decaying viscous boundary layer flow due to a moving sheet two rules the rule of solution expression and the rule of coefficient ergodicity are proposed which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering an explicit analytic solution is given for the first time with recursive formulas for coefficients this analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem

solutions of nonlinear oscillators with fractional powers by an iteration procedure a modified iteration procedure is applied to nonlinear oscillations with fractional powers with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

inner resonance of a coupled hyperbolic tangent nonlinear oscillator arising in a packaging system abstract in this paper a dynamic model of a coupled hyperbolic tangent nonlinear oscillator arising in a packaging system is proposed conditions for resonance are obtained by applying the variational iteration method ii vim ii which should be avoided in the cushioning packaging design moreover the comparison between the vim ii and numerical solutions indicates an excellent agreement

emergence of chaotic behaviour in linearly stable systems strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of lyapunov exponents this regime denoted as stable chaos has been so far mainly characterized by means of numerical studies in this paper we investigate the mechanisms that are at the basis of this form of unpredictable evolution generated by a nonlinear information flow through the boundaries in order to clarify how linear stability can coexist with nonlinear instability we construct a suitable stochastic model in the absence of spatial coupling the model does not reveal the existence of any self sustained chaotic phase nevertheless already this simple regime reveals peculiar differences between the behaviour of finite size and that of infinitesimal perturbations a mean field analysis of the spatially extended case provides a semi quantitative description of the onset of irregular behaviour possible relations with directed percolation as a synchronization transition are also briefly discussed

a new perturbative approach to nonlinear problems a recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the lagrangian such as 4 by 2 1 and then treating as a small parameter it is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the lane emden thomas fermi blasius and duffing equations

the variational iteration method for analytic treatment for linear and nonlinear odes in this work the variational iteration method vim is used for analytic treatment of the linear and nonlinear ordinary differential equations homogeneous or inhomogeneous the method is capable of reducing the size of calculations and handles both linear and nonlinear equations homogeneous or inhomogeneous in a direct manner however for concrete problems a huge number of iterations are needed for a reasonable level of accuracy

proximity of degeneracies and chiral points for complex 2 2 matrices m points of degeneracy d and chiral points c where the eigenvectors are circularly polarized coincide whenm is symmetric and often lie close together when m is not symmetric this proximity is explained statistically by averaging over an ensemble in which the elements of m are random complex numbers the standard deviation of the separation between c and d points is less than half the separation of the two d points if the departure from symmetry is treated as a perturbation of strength e t he separation between c and d points is of order e 2 the probability distribution of the separation is calculated

a numerical algorithm for the solution of telegraph equations abstract in this paper we present a new competitive numerical scheme to solve nonlinear telegraph equations the method is based on rothe s approximation in time discretization and on the wavelet galerkin in the spatial discretization the approximate solutions converge in the space c 0 t l 2 l 2 0 t w 0 1 2 to the variational solution a full error analysis is performed and a numerical experiment is given to illustrate the good convergence behavior of the approximate solution

from synchronization to lyapunov exponents and back the goal of this paper is twofold in the first part we discuss a general approach to determine lyapunov exponents from ensemble rather than time averages the approach passes through the identification of locally stable and unstable manifolds the lyapunov vectors thereby revealing an analogy with generalized synchronization the method is then applied to a periodically forced chaotic oscillator to show that the modulus of the lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase synchronization the analytical calculations are carried out for a model the generalized special flow that we construct as a simplified version of the periodically forced rossler oscillator

on linstedt poincare techniques for the quintic duffing equation abstract an artificial parameter method for the quintic duffing equation is presented the method is based on the introduction of a linear stiffness term and a new dependent variable both of which are proportional to the unknown frequency of oscillation the introduction of an artificial parameter and the expansion of both the solution and the unknown frequency of oscillation in series of the artificial parameter and results in linear ordinary differential equations at each order in the parameter by imposing the nonsecularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation the method does not require that a small parameter be present in the governing equation and its results are compared with those of linstedt poincare modified linstedt poincare harmonic balance and galerkin techniques it is shown that these four techniques predict the same first order approximation to the frequency of oscillation as the artificial parameter method presented in this paper and the latter introduces higher order corrections at second order whereas similar corrections are introduced by the linstedt poincare and modified linstedt poincare methods at orders equal to and higher than three

high order unconditionally stable difference schemes for the riesz space fractional telegraph equation in this paper a class of unconditionally stable difference schemes based on the pade approximation is presented for the riesz space fractional telegraph equation firstly we introduce a new variable to transform the original differential equation to an equivalent differential equation system then we apply a second order fractional central difference scheme to discretize the riesz space fractional operator finally we use 1 1 2 2 and 3 3 pade approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations matrix analysis is used to show the unconditional stability of the proposed algorithms two examples with known exact solutions are chosen to assess the proposed difference schemes numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space fractional hyperbolic equation