random sampling and greedy sparsification for matroid optimization problems random sampling is a powerful tool for gathering information about a group by considering only a small part of it we discuss some broadly applicable paradigms for using random sampling in combinatorial optimization and demonstrate the effectiveness of these paradigms for two optimization problems on matroids finding an optimum matroid basis and packing disjoint matroid bases application of these ideas to the graphic matroid led to fast algorithms for minimum spanning trees and minimum cuts an optimum matroid basis is typically found by agreedy algorithm that grows an independent set into an optimum basis one element at a time this continuous change in the independent set can make it hard to perform the independence tests needed by the greedy algorithm we simplify matters by using sampling to reduce the problem of finding an optimum matroid basis to the problem of verifying that a givenfixed basis is optimum showing that the two problems can be solved in roughly the same time another application of sampling is to packing matroid bases also known as matroid partitioning sampling reduces the number of bases that must be packed we combine sampling with a greedy packing strategy that reduces the size of the matroid together these techniques give accelerated packing algorithms we give particular attention to the problem of packing spanning trees in graphs which has applications in network reliability analysis our results can be seen as generalizing certain results from random graph theory the techniques have also been effective for other packing problems 1998 the mathematical programming society inc published by elsevier science b v

injective stabilization of additive functors ii co torsion and the auslander gruson jensen functor abstract the formalism of injective stabilization of additive functors is used to define a new notion of the torsion submodule of a module it applies to arbitrary modules over arbitrary rings for arbitrary modules over commutative domains it coincides with the classical torsion and for finitely presented modules over arbitrary rings it coincides with the bass torsion a formally dual approach based on projective stabilization gives rise to a new concept the cotorsion quotient module of a module this is done in complete generality the new concept is defined for any module over any ring unlike torsion cotorsion does not have classical prototypes general properties of these constructs are established it is shown that the auslander gruson jensen functor applied to the cotorsion functor returns the torsion functor as a consequence a ring is one sided absolutely pure if and only if each pure injective on the other side is cotorsion free if the injective envelope of the ring is finitely presented then the right adjoint of the auslander gruson jensen functor applied to the torsion functor returns the cotorsion functor this correspondence establishes a duality between torsion and cotorsion over such rings in particular this duality applies to artin algebras it is also shown that over any ring the character module of the torsion of a module is isomorphic to the cotorsion of the character module of the module under various finiteness conditions on the injective envelope of the ring the derived functors of torsion and cotorsion are computed

the numerical analysis of ordinary differential equations runge kutta and general linear methods mathematical and computational introduction the euler method and its generalizations analysis of runge kutta methods general linear methods bibliography

starting algorithms for low stage order rkn methods when second order differential equations are solved with runge kutta nystrom methods the computational effort is dominated by the cost of solving the nonlinear system that is why it is important to have good starting values to begin the iterations in this paper we consider a type of starting algorithms without additional computational cost we study the general order conditions and the maximum order achieved when the runge kutta nystrom method satisfies some simplifying assumptions

a scalable fully implicit compressible euler solver for mesoscale nonhydrostatic simulation of atmospheric flows a fully implicit solver is developed for the mesoscale nonhydrostatic simulation of atmospheric flows governed by the compressible euler equations to spatially discretize the euler equations on a height based terrain following mesh we apply a cell centered finite volume scheme in which an advection upstream splitting ausm up method with a piecewise linear reconstruction is employed to achieve second order accuracy for the low mach flow a second order explicit first step single diagonal coefficient diagonally implicit runge kutta esdirk method with adaptive time stepping is applied to stabilize physically insignificant fast waves and accurately integrate the euler equations in time the nonlinear system arising at each time step is solved by using a jacobian free newton krylov schwarz nks algorithm to accelerate the convergence and improve the robustness we employ a class of additive schwarz preconditioners in which the subdomain jacobian matrix is constructed using a first order spatial discretization several test cases are used to validate the correctness of the scheme and examine the performance of the solver large scale results on a supercomputer with up to 18 432 processor cores are provided to show the parallel performance of the proposed method

independent spanning trees on even networks the use of multiple independent spanning trees ists for data broadcasting in networks provides a number of advantages including the increase of fault tolerance and bandwidth thus the designs of multiple ists on several classes of networks have been widely investigated in this paper we give an algorithm to construct ists on even networks and show that these ists are optimal for height and path lengths and each path in the ists has length at most the length of the shortest path 4 in the even network

high orderp stable formulae for the numerical integration of periodic initial value problems recently there has been considerable interest in the approximate numerical integration of the special initial value problemy f x y for cases where it is known in advance that the required solution is periodic the well known class of stormer cowell methods with stepnumber greater than 2 exhibit orbital instability and so are often unsuitable for the integration of such problems an appropriate stability requirement for the numerical integration of periodic problems is that ofp stability however lambert and watson have shown that ap stable linear multistep method cannot have an order of accuracy greater than 2 in the present paper a class of 2 step methods of runge kutta type is discussed for the numerical solution of periodic initial value problems p stable formulae with orders up to 6 are derived and these are shown to compare favourably with existing methods

linkage of modules abstract it is shown that the notion of linkage of algebraic varieties introduced by peskine and szpiro can be generalized to finitely generated modules over non commutative noetherian semiperfect rings besides greater generality the module theoretic approach brings about new invariants of linkage and yields improved results and simpler proofs even in the traditional settings of commutative algebraic geometry and local algebra connections with auslander reiten sequences singularity theory derived categories local cohomology buchsbaum modules and maximal cohen macaulay approximations are discussed

stabilized starting algorithms for collocation runge kutta methods abstract in this paper we propose a technique to stabilize some starting algorithms often used in the newton type iterations appearing when collocation runge kutta methods are applied to solve stiff initial value problems by following the ideas given in 1 we analyze the order classical and stiff of the new starting algorithms and pay special attention to their error amplifying functions from the computational point of view the new algorithms require the solution of an additional linear system per integration step but as shown in the numerical experiments this extra cost is compensated in most of the problems by their better stability properties

construction of starting algorithms for the rk gauss methods in this paper starting algorithms for the numerical solution of stage equations in runge kutta gauss formulae with 2 3 and 4 stages are constructed for each of these formulae three types of starting algorithms are given according to their requirement of none one or two additional function evaluations per step numerical experiments with hamiltonian systems are presented to show the superior performance of the new starting algorithms of high order

finite element approximation of the cahn hilliard equation with degenerate mobility we consider a fully practical finite element approximation of the cahn hilliard equation with degenerate mobility textstyle frac partial u partial t del b u del gamma lap u psi u where b cdot geq 0 is a diffusional mobility and psi cdot is a homogeneous free energy in addition to showing well posedness and stability bounds for our approximation we prove convergence in one space dimension furthermore an iterative scheme for solving the resulting nonlinear discrete system is analyzed we also discuss how our approximation has to be modified in order to be applicable to a logarithmic homogeneous free energy finally some numerical experiments are presented

a fully spectral methodology for magnetohydrodynamic calculations in a whole sphere abstract we present a fully spectral methodology for magnetohydrodynamic mhd calculations in a whole sphere the use of jones worland polynomials for the radial expansion guarantees that the physical variables remain infinitely differentiable throughout the spherical volume furthermore we present a mathematically motivated and systematic strategy to relax the very stringent time step constraint that is present close to the origin when a spherical harmonic expansion is used for the angular direction the new constraint allows for significant savings even on relatively simple solutions as demonstrated on the so called full sphere benchmark a specific problem with a very accurately known solution the numerical implementation uses a 2d data decomposition which allows it to scale to thousands of cores on present day high performance computing systems in addition to validation results we also present three new whole sphere dynamo solutions that present a relatively simple structure

blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions we describe and test an adaptive algorithm for evolution problems that employs a sequence of blocks consisting of fixed though nonuniform space meshes this approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing remeshing matrix reassembly and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes a major issue with a block adaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy we describe several strategies for achieving this goal using adjoint based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples

packing spanning trees we given an algorithm for packing spanning trees in a graph g v e with capacities on the edges the problem reduces to o v 2 maximum flow computations the algorithm is based on nash williams s proof of a min max relation for this problem

a second order accurate linearized difference scheme for the two dimensional cahn hilliard equation the cahn hilliard equation is a nonlinear evolutionary equation that is of fourth order in space in this paper a linearized finite difference scheme is derived by the method of reduction of order it is proved that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete l2 norm the coefficient matrix of the difference system is symmetric and positive definite so many well known iterative methods e g gauss seidel sor can be used to solve the system

initializers for rk gauss methods based on pseudo symplecticity symplectic runge kutta rk methods for general hamiltonian systems are implicit and an iterative scheme must be used to obtain the solution at each step in this paper the classical order and the pseudo symplecticity order pseudo symplectic runge kutta methods bit 38 1998 439 461 of the one step method that results after s fixed point iterations for solving the implicit equations of stages in an implicit rk method are studied in the numerical experiments with some rk gauss methods s is chosen so that the pseudo symplecticity order is twice the classical order thus the pseudo symplectic method retains some important properties of the original symplectic one further new starting algorithms are constructed taking into account their pseudo symplecticity properties and are compared with other initializers existing in the literature

1 torsion of finite modules over semiperfect rings abstract we initiate the study of 1 torsion of finite modules over two sided noetherian semiperfect rings in particular we give a criterion for determining when the 1 torsion submodule contains minimal generators of the module we also provide an explicit construction for a projective cover of the submodule generated by the torsion elements in the top of the module some of the obtained results hold without the noetherian assumption we also give several applications to local algebra

are high order variable step equistage initializers better than standard starting algorithms in this paper a fourth order starting algorithm for variable step implicit runge kutta methods is developed using the approach of equistage approximation proposed in ima j numer anal 22 2002 153 this starting algorithm is used in combination with the well known radau5 code and numerical results are provided

packing algorithms for arborescences and spanning trees in capacitated graphs in a digraph with real valued edge capacities we pack the greatest number of arborescences in time o n 3m log n 2 m the packing uses at mostm distinct arborescences heren andm denote the number of vertices and edges in the given graph respectively similar results hold for integral packing we pack the greatest number of arborescences in time o min n logn n 2m log n 2 using at mostm n 2 distinct arborescences heren denotes the largest integral capacity of an edge these resuts improve the best previous bounds for capacitated digraphs the algorithm extends to several related problems including packing spanning trees in an undirected capacitated graph and covering such graphs by forests the algorithm provides a new proof of edmonds theorem for arborescence packing for both integral and real capacities based on a laminar family of sets derived from the packing 1998 the mathematical programming society inc published by elsevier science b v

a schwarz waveform moving mesh method an r refinement moving mesh method is considered for solving time dependent partial differential equations pdes the resulting coupled system consisting of the physical pde and a moving mesh pde is solved by a schwarz waveform relaxation method in particular the computational space time domain is decomposed into overlapping subdomains and the solution obtained by iteratively solving the system of pdes on each subdomain dirichlet boundary conditions are used to pass solution information between neighboring regions the efficacy of this approach is demonstrated for some model problems for problems where the solutions evolve on disparate time scales in different regions of the spatial domain this approach demonstrates the significant savings in computational time and effort which are possible

starting algorithms for irk methods in this paper some classes of starting algorithms for the iterations of irk methods are studied they are of three types according to their additional cost by means of b series the order conditions for them are obtained the maximum order attained by these algorithms and their construction are derived too

stage value predictors and efficient newton iterations in implicit runge kutta methods the prediction of stage values in implicit runge kutta methods is important both for overall efficiency as well as for the design of suitable control strategies for the method the purpose of this paper is to construct good stage value predictors for implicit methods and to verify their behavior in practical computations we show that for stiffly accurate methods of low stage order it is necessary to use several predictors in other words a continuous extension for the method will not yield the best results we also investigate how to gain additional efficiency in the newton iterations used to correct the prediction error this leads to new control strategies with respect to refactorization of jacobians that seek to globally minimize total work per unit time of integration

an asymptotically optimal push pull method for multicasting over a random network we consider all cast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session traffic from each node in the session has to be sent to every other node in the session if the session does not consist of all the nodes the remaining nodes act as relays the nodes are connected by undirected links whose capacities are independent and identically distributed random variables we study the asymptotics of the capacity region with network coding in the limit of a large number of nodes and show that the normalized sum rate converges to a constant almost surely we then provide a decentralized push pull algorithm that asymptotically achieves this normalized sum rate without network coding

an improved approximate newton method for implicit runge kutta formulas abstract implicit runge kutta irk methods such as the s stage radau iia method with s 3 5 or 7 for solving stiff ordinary differential equation systems have excellent stability properties and high solution accuracy orders but their high computing costs in solving their nonlinear stage equations have seriously limited their applications to large scale problems to reduce such a cost several approximate newton algorithms were developed including a commonly used one called the simplified newton method in this paper a new approximate jacobian matrix and two new test rules for controlling the updating of approximate jacobian matrices are proposed yielding an improved approximate newton method theoretical and numerical analysis show that the improved approximate newton method can significantly improve the convergence and performance of the simplified newton method

network strength games the core and the nucleolus the maximum number of edge disjoint spanning trees in a network has been used as a measure of the strength of a network it gives the number of disjoint ways that the network can be fully connected this suggests a game theoretic analysis that shows the relative importance of the different links to form a strong network we introduce the network strength game as a cooperative game defined on a graph g v e the player set is the edge set e and the value of a coalition s subseteq e is the maximum number of disjoint spanning trees included in s we study the core of this game and we give a polynomial combinatorial algorithm to compute the nucleolus when the core is non empty

backward error analysis for numerical integrators backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods this is true in particular for the integration of hamiltonian systems where backward error analysis can be used to show that a symplectic method will conserve energy over exponentially long periods of time such results are typically based on two aspects of backward error analysis i it can be shown that the modified vector fields have some qualitative properties which they share with the given problem and ii an estimate is given for the difference between the best interpolating vector field and the numerical method these aspects have been investigated recently for example by benettin and giorgilli in j statist phys 74 1994 pp 1117 1143 by hairer in ann numer math 1 1994 pp 107 132 and by hairer and lubich in numer math 76 1997 pp 441 462 in this paper we aim at providing a unifying framework and a simplification of the existing results and corresponding proofs our approach to backward error analysis is based on a simple recursive definition of the modified vector fields that does not require explicit taylor series expansion of the numerical method and the corresponding flow maps as in the above cited works as an application we discuss the long time integration of chaotic hamiltonian systems and the approximation of time averages along numerically computed trajectories

a note on finding minimum cost edge disjoint spanning trees let g be an undirected graph with n vertices and m edges such that each edge has a real valued cost we consider the problem of finding a set of k edge disjoint spanning trees in g of minimum total edge cost this problem can be solved in polynomial time by the matroid greedy algorithm we present an implementation of this algorithm that runs in o m log m k2n2 time if all edge costs are the same the algorithm runs in o k2n2 time the algorithm can also be extended to find the largest k such that k edge disjoint spanning trees exist in o m2 time we mention several applications of the algorithm

a 17th order radau iia method for package radau applications in mechanical systems a new radau iia code with an order of 17 is programmed for the well known implicit runge kutta program package radau several numerical examples are reported in this article to demonstrate the performance and efficiency of the new algorithm they are real stiff problems obtained from the simulation of mechanical systems

starting algorithms for a class of rk methods for index 2 daes when semiexplicit differential algebraic equations are solved with implicit runge kutta methods rk the computational effort is dominated by the cost of solving the nonlinear systems and therefore it is important to have good starting values to begin the iterations for semiexplicit index 2 daes starting algorithms without additional cost for rk methods with regular matrix coefficient were studied in a previous paper however the regularity condition on the matrix coefficient excludes some interesting methods like lobatto iiia and esdirk methods in this paper we study starting algorithms without additional computational cost for a class of runge kutta methods in the case of index 2 daes

on the construction of error estimators for implicit runge kutta methods for implicit runge kutta methods intended for stiff odes or daes it is often difficult to embed a local error estimating method which gives realistic error estimates for stiff algebraic components if the embedded method s stability function is unbounded at z stiff error components are grossly overestimated in practice some codes improve such inadequate error estimates by premultiplying the estimate by a filter matrix which damps or removes the large stiff error components although improving computational performance this technique is somewhat arbitrary and lacks a sound theoretical backing in this scientific note we resolve this problem by introducing an implicit error estimator it has the desired properties for stiff algebraic components without invoking artificial improvements the error estimator contains a free parameter which determines the magnitude of the error and we show how this parameter is to be selected on the basis of method properties the construction principles for the error estimator can be adapted to all implicit runge kutta methods and a better agreement between actual and estimated errors is achieved resulting in better performance

minimum cuts in near linear time we significantly improve known time bounds for solving the minimum cut problem on undirected graphs we use a semiduality between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques we give a randomized monte carlo algorithm that finds a minimum cut in an m edge n vertex graph with high probability in o m log 3 n time we also give a simpler randomized algorithm that finds all minimum cuts with high probability in o m log 3 n time this variant has an optimal rnc parallelization both variants improve on the previous best time bound of o n 2 log 3 n other applications of the tree packing approach are new nearly tight bounds on the number of near minimum cuts a graph may have and a new data structure for representing them in a space efficient manner

control strategies for the iterative solution of nonlinear equations in ode solvers in the numerical solution of odes by implicit time stepping methods a system of nonlinear equations has to be solved each step it is common practice to use fixed point iterations or in the stiff case some modified newton iteration the convergence rate of such methods depends on the stepsize similarly a stepsize change may force a refactorization of the iteration matrix in the newton solver this paper develops new strategies for handling the iterative solution of nonlinear equations in ode solvers these include automatic switching between fixed point and newton iterations investigating the optimal convergence rate with respect to total work per unit step a strategy for when to reevaluate the jacobian a strategy for when to refactorize the iteration matrix coordination with stepsize control examples will be given showing that the new overall strategy works efficiently in particular the new strategy admits a restrained stepsize variation without refactorizations thus permitting the use of a smoother stepsize sequence the strategy is of equal importance for runge kutta and multistep methods

irk methods for dae starting algorithms abstract when semi explicit differential algebraic equations are solved with implicit runge kutta methods the computational effort is dominated by the cost of solving the nonlinear systems that is why it is important to have good starting values to begin the iterations in this paper we study a type of starting algorithms without additional computational cost in the case of index 1 dae the order of the starting values is defined and by using da series and rooted trees we obtain their general order conditions if the rk satisfies some simplified assumptions then the maximum order can be obtained

computing the strength of a graph the strength of a graph is a measure of its vulnerability strictly generalizing the edge connectivity of a weighted graph cunningham j assoc comput mach 32 1985 pp 549 562 showed how to compute the strength of a graph in o v 4 e time using ideas from polymatroids and network flow in this paper his polymatroid approach is modified a modified version of the goldberg tarjan network flow algorithm j assoc comput mach 4 1988 pp 136 146 is used then using ideas developed by gallo grigoriadis and tarjan siam j comput 18 1989 pp 30 55 and by gusfield martel and fernandez baca in siam j comput 16 1987 pp 237 251 it is shown that the solution runs in o v 3 e time analogous speedups for sparse case bounds are also obtainable

the auslander gruson jensen recollement abstract for any ring r the auslander gruson jensen functor d a fp r mod ab mod r ab op is the exact functor which sends a representable functor x to the tensor functor x we show that this functor admits a fully faithful right adjoint d r and a fully faithful left adjoint d l that is we show that d a is part of a recollement of abelian categories in particular this shows that d a is a localisation and a colocalisation which gives an equivalence of categories fp r mod ab f d a f 0 mod r ab op we show that f d a f 0 is the serre subcategory of fp r mod ab consisting of finitely presented functors which arise from a pure exact sequence as an application of our main result we show that the 0 th right pure derived functor of a finitely presented functor r mod ab is also finitely presented

evaluating numerical ode dae methods algorithms and software until recently the testing of ode dae software has been limited to simple comparisons and benchmarking the process of developing software from a mathematically specified method is complex it entails constructing control structures and objectives selecting iterative methods and termination criteria choosing norms and many more decisions most software constructors have taken a heuristic approach to these design choices and as a consequence two different implementations of the same method may show significant differences in performance yet it is common to try to deduce from software comparisons that one method is better than another such conclusions are not warranted however unless the testing is carried out under true ceteris paribus conditions moreover testing is an empirical science and as such requires a formal test protocol without it conclusions are questionable invalid or even false we argue that ode dae software can be constructed and analyzed by proven standard scientific techniques instead of heuristics the goals are computational stability reproducibility and improved software quality we also focus on different error criteria and norms and discuss modifications to daspk and radau5 finally some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems

an efficient implicit runge kutta method for second order systems abstract we will consider the efficient implementation of a fourth order two stage implicit runge kutta method to solve periodic second order initial value problems to solve the resulting systems we will use the factorization of the discretized operator such proposed factorization involves both complex and real arithmetic the latter case is considered here the resulting system will be efficient and small in size it is one fourth the size of systems using normal implicit runge kutta method numerical details and examples will also be presented to demonstrate the efficiency of the method

adaptive time stepping and computational stability we investigate the effects of adaptive time stepping and other algorithmic strategies on the computational stability of ode codes we show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability a series of computational experiments with the standard implementation of dassl and a modified version including stepsize control based on digital filters is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense the inherent performance and stability of dassl are therefore much greater than the standard implementation seems to suggest

stabilized explicit runge kutta methods for multi asset american options american derivatives have become very popular instruments in financial markets however they are more complicated to price than european options since at each time level we have to determine not only the option value but also whether or not it should be exercised several procedures have been proposed to dissolve these difficulties but they usually involve the solution of nonlinear partial differential equations pdes in the case of multi dimensional problems solving these equations is a very challenging task in this paper we propose stabilized explicit runge kutta serk methods to solve this kind of problems they can easily be applied to many different classes of problems with large dimensions and they have low memory demand since these methods are explicit they do not require algebra routines to solve large nonlinear systems associated to odes as for example lapack and blas packages or multigrid or iterative methods applied together with newton type algorithms and are especially well suited for the method of lines mol discretizations of parabolic pdes

adaptive stepsize based on control theory for stochastic differential equations the numerical solution of stochastic differential equations sdes has been focussed recently on the development of numerical methods with good stability and order properties these numerical implementations have been made with fixed stepsize but there are many situations when a fixed stepsize is not appropriate in the numerical solution of ordinary differential equations much work has been carried out on developing robust implementation techniques using variable stepsize it has been necessary in the deterministic case to consider the best choice for an initial stepsize as well as developing effective strategies for stepsize control the same of course must be carried out in the stochastic case in this paper proportional integral pi control is applied to a variable stepsize implementation of an embedded pair of stochastic runge kutta methods used to obtain numerical solutions of nonstiff sdes for stiff sdes the embedded pair of the balanced milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change the extension of these stepsize controllers from a digital filter theory point of view via pi with derivative pid control will also be implemented the implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy

mono implicit runge kutta schemes for the parallel solution of initial value odes among the numerical techniques commonly considered for the efficient solution of stiff initial value ordinary differential equations are the implicit runge kutta irk schemes the calculation of the stages of the irk method involves the solution of a nonlinear system of equations usually employing some variant of newton s method since the costs of the linear algebra associated with the implementation of newton s method generally dominate the overall cost of the computation many subclasses of irk schemes such as diagonally implicit runge kutta schemes singly implicit runge kutta schemes and mono implicit mirk schemes have been developed to attempt to reduce these costs in this paper we are concerned with the design of mirk schemes that are inherently parallel in that smaller systems of equations are apportioned to concurrent processors this work builds on that of an earlier investigation in which a special subclass of the mirk formulas were implemented in parallel while suitable parallelism was achieved the formulas were limited to some extent because they all had only stage order 1 this is of some concern since in the application of a runge kutta method to a system of stiff odes the phenomenon of order reduction can arise the irk method can behave as if its order were only its stage order or its stage order plus one regardless of its classical order the formulas derived in the current paper represent an improvement over the previous investigation in that the full class of mirk formulas is considered and therefore it is possible to derive efficient parallel formulas of orders 2 3 and 4 having stage orders 2 or 3

a time adaptive finite volume method for the cahn hilliard and kuramoto sivashinsky equations this paper presents a complete finite volume method for the cahn hilliard and kuramoto sivashinsky type of equations the spatial discretization is high order accurate and suitable for general unstructured grids the time integration is addressed by means of implicit an implicit explicit fourth order runge kutta schemes with error control and adaptive time stepping the outcome is a practical accurate and efficient simulation tool which has been successfully applied to accuracy tests and representative simulations the use of adaptive time stepping is of paramount importance in problems governed by the cahn hilliard model an adaptive method may be several orders of magnitude more efficient than schemes using constant or heuristic time steps in addition to driving the simulations efficiently the time adaptive procedure provides a quantitative not just qualitative characterization of the rich temporal scales present in phase separation processes governed by the cahn hilliard phase field model

an efficient jacobi pseudospectral approximation for nonlinear complex generalized zakharov system in this paper we derive an efficient spectral collocation algorithm to solve numerically the nonlinear complex generalized zakharov system gzs subject to initial boundary conditions the jacobi pseudospectral approximation is investigated for spatial approximation of the gzs it possesses the spectral accuracy in space the jacobi gauss lobatto quadrature rule is established to treat the boundary conditions and then the problem with its boundary conditions is reduced to a system of ordinary differential equations in time variable this scheme has the advantage of allowing us to obtain the spectral solution in terms of the jacobi parameters and which therefore means that the algorithm holds a number of collocation methods as special cases finally two illustrative examples are implemented to assess the efficiency and high accuracy of the jacobi pseudo spectral scheme

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result

injective stabilization of additive functors i preliminaries abstract this paper is the first one in a series of three dealing with the concept of injective stabilization of the tensor product and its applications its primary goal is to collect known facts and establish a basic operational calculus that will be used in the subsequent parts this is done in greater generality than is necessary for the stated goal several results of independent interest are also established they include among other things connections with satellites an explicit construction of the stabilization of a finitely presented functor various exactness properties of the injectively stable functors a construction from a functor and a short exact sequence of a doubly infinite exact sequence by splicing the injective stabilization of the functor and its derived functors when specialized to the tensor product with a finitely presented module the injective stabilization with coefficients in the ring is isomorphic to the 1 torsion functor the auslander reiten formula is extended to a more general formula which holds for arbitrary i e not necessarily finite modules over arbitrary associative rings with identity weakening of the assumptions in the theorems of eilenberg and watts leads to characterizations of the requisite zeroth derived functors the subsequent papers provide applications of the developed techniques part ii deals with new notions of torsion module and cotorsion module of a module this is done for arbitrary modules over arbitrary rings part iii introduces a new concept called the asymptotic stabilization of the tensor product the result is closely related to different variants of stable homology these are generalizations of tate homology to arbitrary rings a comparison transformation from vogel homology to the asymptotic stabilization of the tensor product is constructed and shown to be epic