probability estimation in arithmetic and adaptive huffman entropy coders entropy coders such as huffman and arithmetic coders achieve compression by exploiting nonuniformity in the probabilities under which a random variable to be coded takes on its possible values practical realizations generally require running adaptive estimates of these probabilities an analysis of the relationship between estimation quality and the resulting coding efficiency suggests a particular scheme dubbed scaled count for obtaining such estimates it can optimally balance estimation accuracy against a need for rapid response to changing underlying statistics when the symbols being coded are from a binary alphabet simple hardware and software implementations requiring almost no computation are possible a scaled count adaptive probability estimator of the type described in this paper is used in the arithmetic coder of the jbig and jpeg image coding standards

heat equation and its comparative solutions in this paper we will conduct an analytic comparative study between the powerful adomian method and the traditional separation of variables method this is achieved by handling homogeneous and non homogeneous boundary value problem for one dimensional heat equation the study shows the reliability and efficiency of adomian method adomian method provides the solution in a rapidly convergent series through evaluating elegantly computable components

the integration and application of fuzzy and grey modeling methods abstract an integrated fuzzy and grey model and its applications to the prediction control problems are presented the basic grey model gm 1 1 is accompanied with the adaptive fuzzy method to improve its prediction capability the gradient descent scheme is applied to the fuzzy rules to determine whether the predicted results from the grey model should be adjusted the quantity of adjustment is judged from the degrees of the correlation between the past data and the current input we select a few most correlated patterns to decide the direction of adjustment due to the simplicity of the structure and its fast learning characteristics this model is good as a real time controller under the proposed methodology the simulation results are shown to be superior to those systems which exploit complicated control variables and rules a well known difference equation and the weather forecast prediction problems are depicted to verify the superiority of the proposed method

coercive inequalities for gibbs measures abstract we prove the generalized nash and logarithmic nash inequalities for gibbs measures with dirichlet form associated to the kawasaki dynamics

adaptive arithmetic coding using fuzzy reasoning and grey prediction abstract arithmetic coding is an attractive technique for lossless data compression the most important thing in arithmetic coding is to construct a good modeler that always provides accurate probability estimation for incoming data however the characteristics of various types of source data bear a lot of uncertainty and are hard to be extracted so we integrate fuzzy logic and grey theory to develop a smart fuzzy grey tuning modeler to deal with the problem of probability estimation the average compression efficiency of the proposed method is better than other lossless compression methods such as the huffman the approximate arithmetic and the lempel ziv for three types of source data text files image files and binary files besides the design is simple fast and suitable for vlsi implementation since an efficient table look up approach is adopted

new application of adomian decomposition method on fokker planck equation adomian decomposition method has been used for finding the explicit and numerical solutions of the reduced fokker planck equation in a force field the obtained results are compared with those found by other theories such as lie group theory the behaviour of the approximate distribution functions are shown graphically the results of lie group method confirm the correctness of those obtained by adomian decomposition method

a comparison between cole hopf transformation and the decomposition method for solving burgers equations the equation under discussion in this paper is the non linear parabolic burgers equation given by 1 u t uu email protected x x where u u x t in some domain and n is a parameter n 0 and uu x is the non linear term eq 1 is similar in structure to navier stokes equation and has appeared in problems of aerodynamics and was first introduced by j m burgers an equation simply related to 1 appears in the approximate theory of weak non stationary shock wave in a real fluid g adomian solving frontier problems of physics the decomposition method kluwer boston 1994 a wazwaz partial differential equations methods and applications balkema publishers the netherlands 2002 a wazwaz a gorguis an analytic study of fisher s equation by using adomian decomposition methods appl math comput 154 2004 609 620 a wazwaz a gorguis exact solutions for heat like and wave like equations with variable coefficients appl math comput 149 2004 15 29 the coefficient n is a constant that defines the kinematic viscosity if the viscosity n 0 the equation is called inviscid burgers equation which governs gas dynamics the aim of this paper is to study the exact solution of eq 1 in some domain with initial values by the method of cole hopf transformation e hopf the partial differential equation u t uu x u x x comm pure appl math 3 1950 201 230 p lagestrom j d cole l trilling problems in the theory of viscous compressible fluids california institute of technology 1949 which transforms 1 from a non linear partial differential equation into linear heat equation which in turns can be solved exactly we then formally derive the exact solution of 1 with initial and boundary conditions using the adomian decomposition method the comparative study will be conducted to show how reliable sufficient and simpler is the adomian decomposition method

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

an analytic study of fisher s equation by using adomian decomposition method in this paper we develop a framework to obtain exact solutions to fisher s equation and to a nonlinear diffusion equation of the fisher type by employing adomian decomposition method the proposed scheme is supported by examining nonlinear diffusion equations of the fisher type

on the solution of partial differential equations with specified boundary conditions abstract the decomposition method is applied to solution of partial differential equations in two and three dimensions with specified boundary conditions

an exponential time differencing method of lines for burgers fisher and coupled burgers equations abstract an exponential time differencing scheme using the method of lines is developed in this article for the numerical solution of the generalized burgers fisher and coupled burgers equations in each of the aforementioned cases the resulting nonlinear systems are solved explicitly using a second order modified predictor corrector method the efficiency of the method introduced is tested by comparing our experimental results with others selected from the available literature

two boundedness and monotonicity preserving methods for a generalized fisher kpp equation two finite difference methods are proposed for a generalized fisher kpp equation these methods are capable of preserving the skew symmetry of the equation these methods preserve the positivity boundedness and monotonicity of solutions these methods are solvable these methods are convergent a semi explicit finite difference method and an implicit finite difference method are proposed for a generalized fisher kpp equation with two space variables it is proved that these two methods could preserve the skew symmetry of this equation moreover under a condition on the step sizes the semi explicit method is capable of preserving the positivity the boundedness and the spatial and temporal monotonicity of initial approximations and the implicit method is able to preserve these properties with no restriction on the step sizes the stability and convergence of these two methods are also analyzed respectively finally some numerical simulations are provided to verify the validity of our analytical results

a front dynamics approach to curvature dependent flow a front dynamics approach is developed to study the evolution of planar curves whose normal speed depends on curvature the formulation is similar to whitham s shock dynamics theory for the propagation of shock wave in gases but assumes a different propagation rule equations that describe the motion of the front are obtained and these are evolution equations for the normal direction and local arc length of the front the solution of these equations leads to the front positions using an appropriate integration along rays a similarity solution of the equations is found for the evolution of an initial corner free boundary problems for the motion of a junction connecting front segments are discussed a numerical method is presented to calculate the evolution of any number of front segments the segments can be closed or open connected to wall boundaries or not or connected to other segments at 3 segment junctions several sample problems are considered to illustrate the method an extension of the metho

nonplanar traveling fronts in reaction diffusion equations with combustion and degenerate fisher kpp nonlinearities abstract this paper is concerned with nonplanar traveling fronts in reaction diffusion equations with combustion nonlinearity and degenerate fisher kpp nonlinearity our study contains two parts in the first part we establish the existence of traveling fronts of pyramidal shape in r 3 and in the second part we establish the existence and stability of v shaped traveling fronts in r 2

revisit on partial solutions in the adomian decomposition method solving heat and wave equations the adomian decomposition method is considered in application to heat and wave equations the so called partial solution technique is used it is shown that the fundamental equation of the method is well defined only for certain types of boundary conditions in cases involving inhomogeneous boundary conditions improper results may be obtained by former method this paper presents a further insight into partial solutions in the decomposition method and the resolution of such cases

numerical approximation of distributed order reaction diffusion equations in this paper an implicit scheme for the numerical approximation of the distributed order time fractional reaction diffusion equation with a nonlinear source term is presented the stability and the convergence order of the numerical scheme are analysed and illustrated through some numerical examples

an exact solution of a quasilinear fisher equation in cylindrical coordinates lie symmetry method is applied to analyse fisher equation in cylindrical coordinates symmetry algebra is found and symmetry invariance is used to reduce the equation to a first order ode the first order ode is further analysed to obtain exact solution of fisher equation in explicit form

local exponential stabilization of fisher s equation using the backstepping technique abstract this paper deals with the boundary stabilization problem for the 1d fisher s partial differential equation pde defined on a bounded interval which is a nonlinear unstable distributed parameter system the stabilizing controller derived using the backstepping technique for linear parabolic pdes associated with fisher s pde can be extended to the nonlinear case in the work we can prove that the boundary controller based on the linear backstepping synthesis approach can make the closed loop nonlinear fisher s system exponentially stable with any desired decay rate locally in both l 2 0 1 and h 1 0 1 respectively the effectiveness of the control synthesis approach is illustrated by a numerical simulation

on traveling wave solutions of fisher s equation in two spatial dimensions it is shown for the quadratic fisher equation in two spatial dimensions that along with a plane wave there exist several other traveling waves with nontrivial front geometry some of the solutions are found in explicit form others are constructed approximately the dispersion relationship and velocity curvature dependence generated by these solutions are studied

the effects of obstacle size on periodic travelling waves in oscillatory reaction diffusion equations many natural populations undergo multi year cycles and field studies have shown that these can be organized into periodic travelling waves ptws mathematical studies have shown that large scale landscape obstacles represent a natural mechanism for wave generation here we investigate how the amplitude and wavelength of the selected waves depend on the obstacle size we firstly consider a large circular obstacle in an infinite domain for a reaction diffusion system of l u type we use perturbation theory to derive a leading order approximation to the wave generated by the obstacle this shows the dependence of the wave properties on both parameter values and obstacle size we find that the limiting values of the amplitude and wavelength are approached algebraically with distance from the obstacle edge rather than exponentially in the case of a flat boundary we use our results to predict the properties of waves generated by a large circular obstacle for an oscillatory predator prey system via a reduction of the predator prey model to normal form close to hopf bifurcation our predictions compare well with numerical simulations we also discuss the implications of these results for wave stability and briefly investigate the effects of obstacles with elliptical geometries

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

experimentation with two step adomian decomposition method to solve evolution models the two step adomian decomposition method tsadm is derived by separate the standard adomian decomposition method into two steps although the tsadm needs only a slight variation from the standard adomian decomposition method experimentation shows that the tsadm is also promising for systems of inhomogeneous differential and integral equations hyperbolic partial differential equations and singular initial value problems

a note on the stochastic lattice gas model it is proved without imposing translation invariance that the only stationary states for the infinite two dimensional stochastic lattice gas or binary alloy model are the canonical gibbs states and that these dynamics describe a strong return to equilibrium

analytic study on burgers fisher huxley equations and combined forms of these equations abstract in this work we formally derive travelling wave solutions for the burgers fisher huxley equations and combined forms of these equations the tanh coth method is used to determine these sets of travelling wave solutions kinks and periodic wave solutions are constructed the proposed scheme can be used to a wide class of nonlinear evolution equations

analytic and approximate solutions for nagumo telegraph reaction diffusion equation it is known now that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences we generalized nagumo equation to the telegraph reaction diffusion equation and present its analytic approximate solution a by using picard iteration method also using the linear piecewise approximation traveling wave solution are presented the results corresponding to the standard nagumo reaction diffusion equation are regained

algebraic equations with exponential terms abstract the decomposition method is applied to algebraic equations containing exponential terms the n term approximation n is rapidly damped as n increases yielding an oscillating convergence of superior accuracy n 5 and n 9 for k 2

asymptotic equivalence of fluctuation fields for reversible exclusion processes with speed change on considere des processus d exclusion reversibles stationnaires avec changement de vitesse et on etudie la forme asymptotique des champs de fluctuation

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

general solutions with solitary patterns for the defocusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this work the defocusing branch of the genuinely nonlinear dispersive k n n equation that exhibits solutions with solitary patterns is investigated the equation with constant coefficients to the derivatives is examined in one two and three dimensional spaces general formulas for solutions with solitary patterns are developed for all positive integers n n 1 two sets of entirely new formulas one set produces solutions for even integers n whereas the second set produces solutions in opposite directions for odd integers n n 1 are established

pseudospectral method for fisher equation in a disk abstract in this paper we develop a mixed jacobi fourier pseudospectral method for solving the fisher equation in a disc fisher s equation always plays a large role in many fields such as logistic population growth models tissue engineering nuclear reactions and neurophysiology etc it is very important to study how to solve these equations numerically in this work we employ the generalized jacobi approximation to simulate the singularity of solutions at the regional center some mixed jacobi fourier interpolation approximation results are established which play important roles in numerical simulation of various problems defined in a disc as an application the mixed jacobi fourier pseudospectral scheme is provided for the fisher equation in a disk the generalized stability and convergence of the proposed scheme are proved some numerical results are presented to demonstrate the efficiency of this new algorithm

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

adomian decomposition method for solving fractional nonlinear differential equations in this article we have discussed a new application of adomian decomposition method on time fractional nonlinear fractional differential equations three models with fractional time derivative of order a 0 a 1 are considered and solved by means of adomian decomposition method the behaviour of adomian solutions and the effects of different values of a are investigated numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

a pseudospectral method of solution of fisher s equation in this paper we develop an accurate and efficient pseudospectral solution of fisher s equation a prototypical reaction diffusion equation the solutions of fisher s equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient there is an ongoing effort to better adapt pseudospectral methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations the collocation method employed is based on chebyshev gauss lobatto quadrature points we compare results for a single domain as well as for a subdivision of the main domain into subintervals instabilities that occur in the numerical solution for a single domain analogous to those found by others are attributed to round off errors arising from numerical features of the discrete second derivative matrix operator however accurate stable solutions of fisher s equation are obtained with a multidomain pseudospectral method a detailed comparison of the present approach with the use of the sine interpolation is also carried out

nonlinear stability of planar traveling waves in a chemotaxis model of tumor angiogenesis with chemical diffusion abstract we consider a simplified chemotaxis model of tumor angiogenesis described by a keller segel system on the two dimensional infinite cylindrical domain x y r s where s is the circle of perimeter 0 the domain models a virtual channel where newly generated blood vessels toward the vascular endothelial growth factor will be located the system is known to allow planar traveling wave solutions of an invading type in this paper we establish the nonlinear stability of these traveling invading waves when chemical diffusion is present if is sufficiently small the same result for the corresponding system in one dimension was obtained by li li wang 2014 17 our result solves the problem remained open in chae choi kang lee 2018 3 at which only linear stability of the planar traveling waves was obtained under certain artificial assumption

on a class of nonlinear stochastic dynamical systems analysis of the transient behaviour abstract a class of nonlinear dynamical systems with random parameters and initial conditions is considered the transient time evolution of the mean value of the dependent variable is analyzed both by means of the stochastic averaging method and by adomian s decomposition method a proof of the equivalence of the decomposition method to the time series approximation of the dynamical response is provided an application is made to the van der pol equation and finally a comparison between the two previously discussed methods is given

exact solutions for heat like and wave like equations with variable coefficients in this paper adomian decomposition method is presented for solving heat like and wave like models with variable coefficients the method is demonstrated for a variety of problems in one and higher dimensional spaces where exact solutions are obtained the results obtained in all cases show the reliability and the efficiency of this method

haar wavelet method for solving fisher s equation in this paper we develop an accurate and efficient haar wavelet solution of fisher s equation a prototypical reaction diffusion equation the solutions of fisher s equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient there is an ongoing effort to better adapt haar wavelet methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations moreover the use of haar wavelets is found to be accurate simple fast flexible convenient small computation costs and computationally attractive

singularity structure symmetries and integrability of generalized fisher type nonlinear diffusion equation in this letter the integrability aspects of a generalized fisher type equation with modified diffusion in 1 1 and 2 1 dimensions are studied by carrying out a singularity structure and symmetry analysis it is shown that the painleve property exists only for a special choice of the parameter m 2 a backlund transformation is shown to give rise to the linearizing transformation to the linear heat equation for this case m 2 a lie symmetry analysis also picks out the same case m 2 as the only system among this class having a nontrivial infinite dimensional lie algebra of symmetries and that the similarity variables and similarity reductions lead in a natural way to the linearizing transformation and physically important classes of solutions including known ones in the literature thereby giving a group theoretical understanding of the system for nonintegrable cases in 2 1 dimensions associated lie symmetries and similarity reductions are indicated

adaptive numerical method for burgers type nonlinear equations abstract in this paper a moving mesh partial differential equation mmpde approach will be applied to some types of nonlinear partial differential equations the method is described in detail and a number of computational examples are presented using different monitor functions applied to the burgers type equations

fitted reproducing kernel hilbert space method for the solutions of some certain classes of time fractional partial differential equations subject to initial and neumann boundary conditions latterly many problems arising in different fields of science and engineering can be reduced by applying some appropriate discretization to a series of time fractional partial differential equations unlike the normal case derivative the differential order in such equations is with a fractional order which will lead to new challenges for numerical simulation the purpose of this analysis is to introduce the reproducing kernel hilbert space method for treating classes of time fractional partial differential equations subject to neumann boundary conditions with parameters derivative arising in fluid mechanics chemical reactions elasticity anomalous diffusion and population growth models the method provides appropriate representation of the solutions in convergent series formula with accurately computable components numerical experiments with different order derivatives degree are performed to support the theoretical analyses which are acquired by interrupting the n term of the exact solutions finally the obtained outcomes showed that the proposed method is competitive in terms of the quality of the solutions found and is very valid for solving such time fractional neumann problems

stability of planar traveling waves in a keller segel equation on an infinite strip domain abstract we consider a simplified model of tumor angiogenesis described by a keller segel equation on the two dimensional domain x y r s where s is the circle of perimeter it is known that the system allows planar traveling wave solutions of an invading type in case that is sufficiently small we establish the nonlinear stability of traveling wave solutions in the absence of chemical diffusion if the initial perturbation is sufficiently small in some weighted sobolev space when chemical diffusion is present it can be shown that the system is linearly stable lastly we prove that any solution with our front condition eventually becomes planar under certain regularity conditions

general compactons solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this paper we will study the focusing branch of the genuinely nonlinear dispersive k n n equation that exhibits compactons solitons with finite wavelengths the equation will be studied in one two and three dimensional spaces general formulas for compactons solutions are developed for all positive integers n n 1 two sets of entirely new formulas one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n n 1 are established

an analytical study for fisher type equations by using homotopy perturbation method in this paper homotopy perturbation method is applied to fisher type equations the solutions introduced in this study are in recursive sequence forms which can be used to obtain the closed form of the solutions if they are required the method is tested on various examples which are revealing the effectiveness and the simplicity of the method

a modified spectral method for solving operator equations in this paper we introduce a modified spectral method for solving the linear operator equation l u f l d l h 1 h 2 where h 1 and h 2 are normed vector spaces with norms 1 and respectively and d l is the domain of l also for each h h 2 h 2 h h where is an inner product on h 2 in this method we make a new set n n 0 for h 1 using l and two sets in h 1 and h 2 then using the new set n n 0 we solve this linear operator equation we show that this method does not have some shortcomings of spectral method also we prove the stability and convergence of the new method after introducing the method we give some conditions that under them the nonlinear operator equation l u n u f can be solved some examples are considered to show the efficiency of method

efficient multiplication free arithmetic codes arithmetic coding is a powerful lossless data compression technique that has attracted much attention it provides more flexibility and better efficiency than huffman coding does however the multiplications needed in its encoding and decoding algorithms are very undesirable rissanen and mohiuddin 1989 have proposed a simple scheme to avoid the multiplications the present authors found that the performance of their proposed scheme might degrade significantly in some cases they propose a multiplication free multialphabet arithmetic code which can be shown to have minor performance degradation in all cases in the proposed scheme each multiplication is replaced by a single shift and add the authors prove by both theoretical analysis and simulation results that the degradation of the proposed multiplication free scheme is always several times 2 7 times in the present experiments smaller than that of the rissanen mohiuddin s scheme

semilinear stochastic systems analysis with the method of the stochastic green s function and application in mechanics abstract this work deals with the analysis of a class of semilinear vector stochastic operator equations the method of the stochastic green s function due to adomian is extended to the above mentioned class of equations some perturbation techniques are also developed and a pertinent application in nonlinear mechanics is considered

conditional full stability of positivity preserving finite difference scheme for diffusion advection reaction models this work has been partially supported by the ministerio de economia y competitividad spanish grant mtm2017 89664 p

coupled nonlinear stochastic differential equations abstract systems of n coupled linear or nonlinear differential equations which may be deterministic or stochastic are solved by methods of the first author and his co workers examples include two coupled riccati equations coupled linear equations stochastic coupled equations with product terms and n coupled stochastic differential equations

fisher equation for anisotropic diffusion simulating south american human dispersals the fisher equation is commonly used to model population dynamics this equation allows describing reaction diffusion processes considering both population growth and diffusion mechanism some results have been reported about modeling human dispersion always assuming isotropic diffusion nevertheless it is well known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations solutions to a fisher equation are difficult to obtain for complex geometries moreover when anisotropy has to be considered and so few studies have been conducted in this direction with this scope in mind we present in this paper a solution for a fisher equation introducing anisotropy we apply a finite difference method using the crank nicholson approximation and analyze the results as a function of the characteristic parameters finally this methodology is applied to model south american human dispersal

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation abstract nonlinear evolution equations nees are very important partial differential equations in nonlinear physics optics and engineering in this article we apply the residual power series rps method to the initial value problem of the nonlinear spatial conformable fractional evolution equations coefficients of the analytic solution are computed by recursive formulae and the famous nonlinear spatial conformable fractional fisher equation is taken as an example to verify this method direct computations demonstrate the correctness of the recursive formulae meanwhile the recursive formulae can be easily implemented by mathematical software

curved fronts in the belousov zhabotinskii reaction diffusion systems in r 2 in this paper we consider a diffusion system with the belousov zhabotinskii bz for short chemical reaction following brazhnik and tyson 4 and perez munuzuri et al 45 who predicted v shaped fronts theoretically and discovered v shaped fronts by experiments respectively we give a rigorous mathematical proof of their results we establish the existence of v shaped traveling fronts in r 2 by constructing a proper supersolution and a subsolution furthermore we establish the stability of the v shaped front in r 2 c 2018 elsevier inc all rights reserved