an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

regularization methods for solving differential algebraic equations in m knorrenschild siam j numer anal 29 1992 1694 1715 a class of regularization methods for solving autonomous index 1 daes differential algebraic equations has been proposed in this paper we generalize it to non autonomous index 1 and higher index daes we will treat a daes as an infinitely stiff odes ordinary differential equations therefore the solutions of a daes can be considered as the limit of the solutions of the corresponding stiff odes in some sense some similar results with m knorrenschild 1992 loc cit are obtained

complete blow up after tmax for the solution of a semilinear heat equation soit un sous ensemble ouvert borne de r n a frontiere lisse on considere le probleme u t u f u dans o t u 0 sur o t u x o u 0 x x ou f r r est localement de lipschitz non decroissante et f o 0

on the numerical solution of differential algebraic equations by pade series in this paper the solution for a differential algebraic equation dae can be expanded up to arbitrary order using maple computer algebra systems frank maple v crc press boca raton fl 1996 first we calculate power series of the given equations system then transform it into pade series form which gives an arbitrary order for solving dae numerically

the existence of bounded solutions of a semilinear elliptic equation on etudie l existence de la solution non constante bornee de l equation differentielle w y w 2 w p 1 w w p 1 0 dans r n n2 avec pp c ou p c n 2 n 2 est l exposant de l espace de sobolev critique pour r n

sequential regularization methods for nonlinear higher index daes sequential regularization methods relate to a combination of stabilization methods and the usual penalty method for differential equations with algebraic equality constraints this paper extends an earlier work siam j numer anal 33 1996 pp 1921 1940 to nonlinear problems and to differential algebraic equations daes with an index higher than 2 rather than having one winning method this is a class of methods from which a number of variants are singled out as being particularly effective methods in certain circumstances we propose sequential regularization methods for index 2 and index 3 daes both with and without constraint singularities in the case of no constraint singularity we prove convergence results numerical experiments confirm our theoretical predictions and demonstrate the viability of the proposed methods the examples include constrained multibody systems

on the uniqueness of l1 continuation after blowup abstract this paper is concerned with the uniqueness of l 1 continuation beyond blowup for a cauchy problem of a semilinear heat equation p u t u u p in r n 0 t u x 0 u 0 x 0 in r n with p 1 0 t and u 0 l r n here we say that u is an l 1 solution of p if u c 0 t l loc 1 r n with u l loc p r n 0 t satisfies p in the distributional sense in the case of p s p p jl a counter example for the uniqueness of radial l 1 solution of p after blowup was given in m fila n mizoguchi multiple continuation beyond blow up differential integral equations 20 2007 671 680 where p s and p jl are the exponent of sobolev and of joseph and lundgren respectively we give a sufficient condition for the uniqueness of l 1 continuation beyond blowup for p p jl in the radial case if for an l 1 solution u of p there exists a sequence u n of classical solutions of p such that u 0 n u 0 in l r n as n for the sequence u 0 n of initial data and that u n t u t in l loc p r n as n for t 0 t then u is called a limit l 1 solution based on the sufficient condition we prove the uniqueness of limit l 1 solution with radial symmetry after blowup for p p jl

wavelet operational matrix method for solving fractional differential equations with variable coefficients abstract in this paper another operational matrix method based on haar wavelet is proposed to solve the fractional differential equations with variable coefficients the haar wavelet operational matrix of fractional order integration is derived without using the block pulse functions considered in li and zhao 2010 1 the operational matrix of fractional order integration is utilized to reduce the initial equations to a system of algebraic equations some examples are included to demonstrate the validity and applicability of the method moreover compared with the known technique the methodology is shown to be much more efficient and accurate

when the mean is not enough calculating fixation time distributions in birth death processes studies of fixation dynamics in markov processes predominantly focus on the mean time to absorption this may be inadequate if the distribution is broad and skewed we compute the distribution of fixation times in one step birth death processes with two absorbing states these are expressed in terms of the spectrum of the process and we provide different representations as forward only processes in eigenspace these allow efficient sampling of fixation time distributions as an application we study evolutionary game dynamics where invading mutants can reach fixation or go extinct we also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states whereas the mean fixation time has no such interpretation

continuation of blowup solutions of nonlinear heat equations in several space dimensions the possible continuation of solutions of the nonlinear heat equation in r n r ut u m u p with m 0 p 1 after the blowup time is studied and the different continuation modes are discussed in terms of the exponents m and p thus for m p 2 we find a phenomenon of nontrivial continuation where the regionfx u x t 1g is bounded and propagates with finite speed this we call incomplete blowup for n 3 and p m n 2 n 2 we find solutions that blow up at finite t t and then become bounded again for t t otherwise we find that blowup is complete for a wide class of initial data in the analysis of the behavior for large p a list of critical exponents appears whose role is described we also discuss a number of related problems and equations we apply the same technique of analysis to the problem of continuation after the onset of extinction for example for the equation ut u m u p m 0

on the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity this paper is concerned with a cauchy problem mbox p left begin array ll u t delta u u p quad mbox in bf r n times 0 infty u x 0 lambda varphi x quad mbox in bf r n end array right where p p ast equiv n 2 n 2 lambda 0 and varphi is a nonnegative radially symmetric function in c 1 bf r n with compact support denote the solution of p by u lambda let p ast infty if 3 leq n leq 10 and p ast 1 6 n 10 if n geq 11 we show that if p ast p p ast then there is lambda varphi 0 such that i if lambda lambda varphi then u lambda exists globally in time in the classical sense and u lambda t converges to zero locally uniformly in bf r n as t to infty ii if lambda lambda varphi then u lambda blows upincompletely in finite time iii if lambda lambda varphi then u lambda blows upcompletely in finite time

adomian decomposition method for solution of differential algebraic equations solutions of differential algebraic equations is considered by adomian decomposition method in e babolian m m hosseini reducing index and spectral methods for differential algebraic equations j appl math comput 140 2003 77 and m m hosseini an index reduction method for linear hessenberg systems j appl math comput in press an efficient technique to reduce index of semi explicit differential algebraic equations has been presented in this paper adomian decomposition method is applied to reduced index problems the scheme is tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

haar wavelet method for solving fractional partial differential equations numerically in this paper a wavelet operational method based on haar wavelet is proposed to solve the fractional partial differential equations in the caputo derivative sense we give the haar wavelet operational matrix of fractional order integration a truncated haar wavelet series together with the wavelet operational matrix are utilized to reduce the fractional partial differential equations to sylvester equations in addition some examples are presented to show the efficiency and the accuracy of the approach

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

analytical approximate solutions of systems of fractional algebraic differential equations by homotopy analysis method abstract in this paper we develop a framework to obtain approximate solutions to systems of algebraic differential equations of fractional order by employing the homotopy analysis method ham the study highlights the efficiency of the method and its dependence on the auxiliary parameter numerical examples are examined to highlight the significant features of the ham method the method shows improvements over existing analytical techniques

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

block pulse operational matrix method for solving fractional partial differential equation in this paper we first introduce two dimensional block pulse functions and the block pulse operational matrices of the fractional order integration also the block pulse operational matrices of the fractional order differentiation are obtained then we present a computational method based on the above results for solving a class of fractional partial differential equations transforming the initial equation into a sylvester equation the error analysis of the method is given the method is computationally attractive and applications are demonstrated by some numerical examples moreover comparing the methodology with the known technique shows that our approach is more efficient and more convenient

walds martingale and the conditional distributions of absorption time in the moran process many models of evolution are stochastic processes where some quantity of interest fluctuates randomly in time one classic example is the moranbirthdeath process where that quantity is the number

multiple blow up for a porous medium equation with reaction the present paper is concerned with the cauchy problem left begin array ll partial t u delta u m u p quad rm in mathbb r n times 0 infty u x 0 u 0 x geq 0 quad rm in mathbb r n end array right with p m 1 a solution u with bounded initial data is said to blow up at a finite time t if lim rm sup t nearrow t u t l infty mathbb r n infty for n 3 we obtain in a certain range of values of p weak solutions which blow up at several times and become bounded in intervals between these blow up times we also prove a result of a more technical nature proper solutions are weak solutions up to the complete blow up time

explicit inverses of some tridiagonal matrices abstract we give explicit inverses of tridiagonal 2 toeplitz and 3 toeplitz matrices which generalize some well known results concerning the inverse of a tridiagonal toeplitz matrix

various behaviors of solutions for a semilinear heat equation after blowup abstract the present paper is concerned with a cauchy problem for a semilinear heat equation p u t u u p in r n 0 u x 0 u 0 x 0 in r n we show that if p n 2 n 1 n 4 2 n 1 and n 11 then there exists a solution u i i 1 2 3 of p which blows up at t t i becomes a regular solution for all t t i and behaves as follows i lim t u 1 t 0 ii 0 lim inf t u 2 t lim sup t u 2 t iii lim t u 3 t where denotes the supremum norm in r n

evolutionary games on cycles with strong selection evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success quantified by the probability that a single mutant takes over a population graph structures compared to the well mixed case can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant properties of the associated mean fixation times can be more intricate especially when selection is strong the intuition is that fixation of a beneficial mutant happens fast in a dominance game that fixation takes very long in a coexistence game and that strong selection eliminates demographic noise here we show that these intuitions can be misleading in structured populations we analyze mean fixation times on the cycle graph under strong frequency dependent selection for two different microscopic evolutionary update rules death birth and birth death we establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size depending on the underlying game we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring death birth update in contrast if selection for an offspring occurs before random removal birth death update then strong selection can remove demographic noise almost entirely

multiple blowup of solutions for a semilinear heat equation ii abstract the present paper is concerned with a cauchy problem for a semilinear heat equation p u t u u p in r n 0 u x 0 u 0 x 0 in r n with p 1 and u 0 l r n we show that if p n 2 n 1 n 4 2 n 1 and n 11 then for each positive integer n 2 there exist t i 0 i 1 2 n with t 1 t 2 t n and a global l 1 solution u of p such that u is a regular solution of p for t 0 t 1 t 2 t n and blows up at t t i for i 1 2 n

fixation time in evolutionary graphs a mean field approach using an analytical method we calculate average conditional fixation time of mutants in a general graph structured population of two types of species the method is based on markov chains and uses a mean field approximation to calculate the corresponding transition matrix analytical results are compared with the results of simulation of the moran process on a number of network structures

analytical calculation of average fixation time in evolutionary graphs the ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics fixation probability and average fixation time aft are two important parameters to quantify this ability in this paper we introduce an analytical approach for exact calculation of aft using this method we obtain aft for two types of evolutionary graphs cycle graph as a highly homogeneous graph and star graph as a highly heterogeneous graph we use symmetries of these graphs to calculate aft analytical results are confirmed with simulation we also examine the effect of adding some random edges to each of these structures

blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity abstract this paper is concerned with blowup phenomena of solutions for the cauchy and the cauchy dirichlet problem of p u t u u p with p in the supercritical range in the sense of sobolev s embedding we first show that if p 1 7 n 11 and n 12 then there are no radially symmetric bounded positive solutions of w y 2 w 1 p 1 w w p 0 in r n which intersect the radially symmetric singular solution at least twice using the above result the existence of a blowup solution of type ii for the cauchy dirichlet problem for p in a ball is proved where a solution u is said to exhibit the type ii blowup at t t if lim sup t t t t 1 p 1 u t

fitness dependence of the fixation time distribution for evolutionary dynamics on graphs evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and nonmutant individuals recent studies have found that fixation times in such systems often have right skewed distributions little is known however about how these distributions and their skew depend on mutant fitness here we calculate the fitness dependence of the fixation time distribution for the moran birth death process in populations modeled by two extreme networks the complete graph and the one dimensional ring lattice obtaining exact solutions in the limit of large network size we find that with non neutral fitness the moran process on the ring has normally distributed fixation times independent of the relative fitness of mutants and nonmutants in contrast on the complete graph the fixation time distribution is a fitness weighted convolution of two gumbel distributions when fitness is neutral the fixation time distribution jumps discontinuously and becomes highly skewed on both the complete graph and the ring even on these simple networks the fixation time distribution exhibits a rich fitness dependence with discontinuities and regions of universality extensions of our results to two fitness moran models times to partial fixation and evolution on random networks are discussed

efficient runge kutta integrators for index 2 differential algebraic equations in seeking suitable runge kutta methods for differential algebraic equations we consider singly implicit methods to which are appended diagonally implicit stages methods of this type are either similar to those of butcher and cash or else allow for the importation of a final derivative from a previous step for these two classes with up to three additional diagonally implicit stages we derive methods that satisfy appropriate order conditions for index 2 daes

convergence of adomian s decomposition method periodic temperatures abstract the convergence of adomian s decomposition method 1 as applied to periodic temperature fields in heat conductors is investigated

numerical solutions of nonlinear fractional differential equations by alternative legendre polynomials abstract in this paper numerical techniques are presented for solving initial value problems of nonlinear fractional differential equations the method is implemented by applying alternative legendre polynomials the operational matrix of fractional integration and the product for the alternative legendre polynomials are derived in order to transform the nonlinear equations into a system of algebraic equations the study of the error analysis of the obtained method is also considered furthermore numerical examples demonstrate that this method is applicable and accurate

adomian decomposition method for solution of nonlinear differential algebraic equations in m m hosseini adomian decomposition method with chebyshev polynomials appl math comput in press an efficient modification of the adomian decomposition method was presented by using chebyshev polynomials also in m m hosseini adomian decomposition method for solution of differential algebraic equations j comput appl math in press solution of linear differential algebraic equations was considered by adomian decomposition method in this paper standard and modified adomian decomposition methods are applied to non linear differential algebraic equations the schemes are tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

multiple blowup of solutions for a semilinear heat equation the present paper is concerned with a cauchy problem for a semilinear heat equation open image in new window with u0 l rn a solution u of p is said to blow up at t t if lim supt t u t with the supremum norm in rn we show that if open image in new window and n 11 then there exists a proper solution u of p which blows up at t t1 becomes a regular solution for t t1 t2 and blows up again at t t2 for some t1 t2 with 0 t1 t2

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

an index reduction method for linear hessenberg systems in e babolian m m hosseini reducing index and pseudospectral methods for differential algebraic equations appl math comput 140 2003 77 90 a reducing index method has been proposed for some cases of semi explicit daes differential algebraic equations in this paper this method is generalized to more cases also it is focused on hessenberg index 2 systems and proposed reduction index method will be illustrated for this problem the hessenberg system and its obtained reduced index system are numerically solved through pseudospectral method in addition aforementioned methods will be considered by one example

numerical solution of linear differential algebraic equations in appl math comput 140 2003 77 and appl math comput in press a reducing and modified reducing index methods have been proposed for some cases of semi explicit daes differential algebraic equations in this paper these methods are generalized to more cases also numerical implementation of generalized methods will be presented through pseudospectral method with domain decomposition in addition aforementioned methods will be considered by some examples

levinthal s paradox abstract levinthal s paradox is that finding the native folded state of a protein by a random search among all possible configurations can take an enormously long time yet proteins can fold in seconds or less mathematical analysis of a simple model shows that a small and physically reasonable energy bias against locally unfavorable configurations of the order of a few kt can reduce levinthal s time to a biologically significant size

adomian decomposition method with chebyshev polynomials in this paper an efficient modification of the adomian decomposition method is presented by using chebyshev polynomials the proposed method can be applied to linear and non linear models the scheme is tested for some examples and the obtained results demonstrate reliability and efficiency of the proposed method