fractal basin boundaries abstract basin boundaries for dynamical systems can be either smooth or fractal this paper investigates fractal basin boundaries one practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes the structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected examples and discussion of both types of structures are given and it appears that fractal basin boundaries should be common in typical dynamical systems lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed

a constrained min max algorithm for rival models of the same economic system there are well established rival theories about the economy these have in turn led to the development of rival models purporting to represent the economic system the models are large systems of discrete time nonlinear dynamic equations observed data of the real system does not in general provide sufficient information for statistical methods to invalidate all but one of the rival models in such a circumstance there is uncertainty about which model to use in the formulation of policy prudent policy design would suggest that a model based policy should take into account all the rival models this is achieved as a pooling of the models the pooling that yields the policy which is robust to model choice is formulated as a constrained min max problem the minimization is over the decision variables and the maximization is over the rival models only equality constraints are considered

the time line interpolation method for large time step godunov type schemes abstract this paper describes the use of the time line interpolation procedure for the design of large time step godunov type schemes for systems of hyperbolic conservation laws in one dimension these schemes are based on a specific procedure to characterize the left and right states of the riemann problems at the cell interfaces when the courant number associated with the waves exceeds unity to do so the time line interpolation technique is used constant and linear reconstruction techniques are presented sonic or critical points are seen to be a source of difficulty in the algorithm and an appropriate treatment is proposed the algorithms are applied to the linear advection equation to the inviscid burgers equation and to the set of hyperbolic conservation laws that describe shallow water flow in one dimension these simulations show the superiority of the linear time reconstruction over the use of a constant time reconstruction when the linear reconstruction technique is used the modulus of the amplification factor of the scheme is equal to unity for all wave numbers inducing oscillations in the computed profile owing to the phase error the introduction of a slope limiter allows these oscillations to be eliminated but yields numerical diffusion thus restricting the range of applications of the scheme

a new norm relaxed method of strongly sub feasible direction for inequality constrained optimization combining the norm relaxed method of feasible direction mfd with the idea of strongly sub feasible direction method we present a new convergent algorithm with arbitrary initial point for inequality constrained optimization at each iteration the new algorithm solves one direction finding subproblem dfs which always possesses a solution some good properties of the new algorithm are that it can unify automatically the operations of initialization phase i and optimization phase ii and the number of the functions satisfying the inequality constrains is nondecreasing particularly a feasible direction of descent can be obtained by solving dfs whenever the iteration point gets into the feasible set under some mild assumptions without the linear independence the global and strong convergence of the algorithm can be obtained

the method of space time conservation element and solution element a new approach for solving the navier stokes and euler equations a new numerical framework for solving conservation laws is being developed this new framework differs substantially in both concept and methodology from the well established methods i e finite difference finite volume finite element and spectral methods it is conceptually simple and designed to overcome several key limitations of the above traditional methods a two level scheme for solving the convection diffusion equation u t a u x 2u x2 0 0 is constructed and used to illuminate major differences between the present method and those mentioned above this explicit scheme referred to as the a scheme has two independent marching variables unj and ux nj which are the numerical analogues of u and u x at j n respectively the a scheme has the unusual property that its stability is limited only by the cfl condition i e it is independent of also it can be shown that the amplification factors of the a scheme are identical to those of the leapfrog scheme if o and to those of the dufort frankel scheme if a o these coincidences are unexpected because the a scheme and the above classical schemes are derived from completely different perspectives and the a scheme does not reduce to the above classical schemes in the limiting cases the a scheme is extended to solve the 1d time dependent navier stokes equations of a perfect gas stability of this explicit solver also is limited only by the cfl condition in spite of the fact that it does not use i any techniques related to the high resolution upwind methods and ii any ad hoc parameter the current navier stokes solver is capable of generating highly accurate shock tube solutions particularly for high reynolds number flows shock discontinuities can be resolved within one mesh interval the inviscid 0 a scheme is reversible in time it also is neutrally stable i e free from numerical dissipation such a scheme generally cannot be extended to solve the euler equations thus the inviscid version is modified stability of this modified scheme referred to as the a scheme is limited by the cfl condition and 0 1 where is a special parameter that controls numerical dissipation moreover if 0 the amplification factors of the a scheme are identical to those of the leapfrog scheme which has no numerical dissipation on the other hand if 1 the two amplification factors of the a scheme become the same function of the courant number and the phase angle unexpectedly this function also is the amplification factor of the highly diffusive lax scheme note that because the lax scheme is very diffusive and it uses a mesh that is staggered in time a two level scheme using such a mesh is often associated with a highly diffusive scheme the a scheme which also uses a mesh staggering in time demonstrates that it can also be a scheme with no numerical dissipation the euler extension of the a scheme has stability conditions similar to those of the a epsiv scheme itself it has the unusual property that numerical dissipation at all mesh points can be controlled by a set of local parameters moreover it is capable of generating accurate shock tube solutions with the cfl number ranging from close to 1 to 0 022

algorithms for determination of period doubling bifurcation points in ordinary differential equations abstract four algorithms for evaluating period doubling bifurcation points in periodic solutions of autonomous systems of ordinary differential equations are presented two of the algorithms can also be used for nonautonomous systems the algorithms are applied to three examples two interconnected reaction cells the lorenz model and a reactor with periodic forcing convergence properties of the algorithms are shown and a number of computed bifurcation points are presented convergence of the feigenbaum sequence is shown for a period doubling cascade in the lorenz model

finite volume treatment of dispersion relation preserving and optimized prefactored compact schemes for wave propagation in developing suitable numerical techniques for computational aero acoustics the dispersion relation preserving drp scheme by tam and co workers and the optimized prefactored compact opc scheme by ashcroft and zhang have shown desirable properties of reducing both dissipative and dispersive errors these schemes originally based on the finite difference attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre determined formal orders of accuracy in the present study finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications linear and nonlinear wave equations with and without viscous dissipation have been adopted as the test problems highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases the performance of these approaches is documented for the linear wave equation there is no major difference between the drp and opc schemes for the nonlinear wave equations the finite volume version of both drp and opc schemes offers substantially better solutions in regions of high gradient or discontinuity

a sequential quadratically constrained quadratic programming method for unconstrained minimax problems in this paper a sequential quadratically constrained quadratic programming sqcqp method for unconstrained minimax problems is presented at each iteration the sqcqp method solves a subproblem that involves convex quadratic inequality constraints and a convex quadratic objective function the global convergence of the method is obtained under much weaker conditions without any constraint qualification under reasonable assumptions we prove the strong convergence superlinearly and quadratic convergence rate

an examination of initial condition maps for the sinusoidally excited buckled beam modeled by the duffing s equation abstract the initial condition problem is studied for the dynamics of the buckled beam by using the forced holmes duffing s equation in an attempt to understand the route to chaos earlier results generated by moon 1 for different parameter values are reconsidered and new techniques are used in order to understand more of the global behavior of the system in particular fractal basin boundaries are determined for two types of basins of attraction these are correlated with previous results to help provide an explanation for observed chaotic system behavior

a feasible descent sqp algorithm for general constrained optimization without strict complementarity in this paper a class of optimization problems with equality and inequality constraints is discussed firstly the original problem is transformed to an associated simpler problem with only inequality constraints and a parameter the later problem is shown to be equivalent to the original problem if the parameter is large enough but finite then a feasible descent sqp algorithm for the simplified problem is presented at each iteration of the proposed algorithm a master direction is obtained by solving a quadratic program which always has a feasible solution with two corrections on the master direction by two simple explicit formulas the algorithm generates a feasible descent direction for the simplified problem and a height order correction direction which can avoid the maratos effect without the strict complementarity then performs a curve search to obtain the next iteration point thanks to the new height order correction technique under mild conditions without the strict complementarity the globally and superlinearly convergent properties are obtained finally an efficient implementation of the numerical experiments is reported

regular article the space time conservation element and solution element method a new high resolution and genuinely multidimensional paradigm for solving conservation laws a new high resolution and genuinely multidimensional numerical method for solving conservation laws is being developed it was designed to avoid the limitations of the traditional methods and was built from ground zero with extensive physics considerations nevertheless its foundation is mathematically simple enough that one can build from it a coherent robust efficient and accurate numerical framework two basic beliefs that set the new method apart from the established methods are at the core of its development the first belief is that in order to capture physics more efficiently and realistically the modeling focus should be placed on the original integral form of the physical conservation laws rather than the differential form the latter form follows from the integral form under the additional assumption that the physical solution is smooth an assumption that is difficult to realize numerically in a region of rapid change such as a boundary layer or a shock the second belief is that with proper modeling of the integral and differential forms themselves the resulting numerical solution should automatically be consistent with the properties derived from the integral and differential forms e g the jump conditions across a shock and the properties of characteristics therefore a much simpler and more robust method can be developed by avoiding the explicit use of the above derived properties specifically to capture physics as fully as possible the method requires that i space and time be unified and treated as a single entity ii both local and global flux conservation in space and time be enforced and iii a multidimensional scheme be constructed without using the dimensional splitting approach such that multidimensional effects and source terms which are scalars can be modeled more realistically to simplify mathematics and broaden its applicability as much as possible the method attempts to use the simplest logical structures and approximation techniques specifically i it uses a staggered space time mesh such that flux at any interface separating two conservation elements can be evaluated internally in a simpler and more consistent manner without using a separate flux model ii it avoids the use of many well established techniques such as riemann solvers flux splittings and monotonicity constraints such that the complications and possibly even the limitations associated with them may be avoided and iii it avoids the use of special techniques that are not applicable to more general problems furthermore triangles in 2d space and tetrahedrons in 3d space are used as the basic building blocks of the spatial meshes such that the method i can be used to construct 2d and 3d nondissipative schemes in a natural manner and ii is compatible with the simplest unstructured meshes note that while numerical dissipation is required for shock capturing it may also result in annihilation of small disturbances such as sound waves and in the case of flow with a large reynolds number may overwhelm physical dissipation to overcome this difficulty two different and mutually complementary types of adjustable numerical dissipation are introduced in the present development

researches on chaos phenomenon of eeg dynamics model according to phase space reconstruct technique from one dimensional time series and the quantitative criterion and rule of system chaos analyses and computations are conducted on eeg electroencephalogram dynamics model based on the comparative studies of the phase graph the power spectra the computation of the correlation dimension and the lyapunov exponent to eeg signals from the model the following conclusions are shown i chaotic patterns of the dynamics model may emerge out of pomeau manneville route and relevant to double periodic bifurcation hopf bifurcation and reverse bifurcation ii to further support the view that chaos exist in eeg signals

a local space time conservation scheme and its application in shock wave propagation abstract in this paper a local space time conservation scheme based on non staggered grids is introduced which is a variation of space time conservation element and solution element ce se scheme it inherits most features and advantages of ce se method including unified treatment of space and time and high accuracy resolution of hyperbolic conservation equations moreover riemann solvers are not needed to capture shocks and dimensional splitting methods are not needed in the multi dimensional schemes the stability of the present scheme is verified through von neumann analysis moreover several shock wave problems including one two and three dimensional cases are simulated by the present scheme by carefully comparing the present scheme s numerical results with exact solutions experimental results original ce se scheme s numerical results and third order eno scheme s numerical results it can be conclude that the present scheme is efficient and accurate

computational considerations for the simulation of shock induced sound the numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm because it requires the ability to propagate disturbances of small amplitude and short wavelength the demands are particularly high when shock waves are involved because the chosen algorithm must also resolve discontinuities in the solution the extent to which a high order accurate shock capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified such a study is initiated in this work a fourth order accurate essentially nonoscillatory eno method is used to investigate the solutions of inviscid compressible flows with shocks the design order of accuracy is achieved in the smooth regions of a steady state quasi one dimensional test case however in an unsteady test case only first order results are obtained downstream of a sound shock interaction the difficulty in obtaining a globally high order accurate solution in such a case with a shock capturing method is demonstrated through the study of a simplified linear model problem some of the difficult issues and ramifications for aeroacoustic simulations of flows with shocks that are raised by these results are discussed

a continuation algorithm for discovering new chaotic motions in forced duffing systems we study a dynamical system described by the duffing equation under static plus large periodic excitation the bifurcation diagram in terms of the amplitude of the periodic excitation reveals that there are at least six cascades of period doubling bifurcations with the other parameters fixed at specific values these six sequences are further investigated by a continuation algorithm which is based on the principles of the shooting method combined with the newton method for solving nonlinear equations a runge kutta huta method has been used for solving the system of differential equations the final conclusion is that each of the six sequences is governed by feigenbaum s number 4 6692 from universality theory beyond the limit values derived for the amplitude of the periodic excitation new strange attractors are found

application of high order difference methods for the study of period doubling bifurcations in nonlinear oscillators abstract for the study of period doubling bifurcations in nonlinear t periodic forced oscillators depending on one parameter it is necessary to use a quick and accurate method to obtain periodic solutions of a second order nonlinear differential equation using a periodic approximation obtained earlier for another parametric value a newton method allows its iterative refinement by the successive solution of linear periodic boundary value problems in these problems the derivatives of the unknown periodic solution are approximated by high order difference formulae yielding accurate results in the n abscissae x i it n i 0 n 1 to determine the parametric values where bifurcation takes place the solution of the variational equations was calculated using a runge kutta h ta method therefore the values of the corresponding nt periodic solution n 2k k n were determined in some points inside the discretization intervals using trigonometric interpolation from the resulting fundamental matrix nt the multipliers are readily determined allowing the detection of the period doubling bifurcations when the largest multiplier passes through 1 the method has been applied successfully to study bifurcations leading to chaos in several classical nonlinear oscillators

application of space time ce se method to shallow water magnetohydrodynamic equations in this article we apply a space time conservation element and solution element ce se method for the approximate solution of shallow water magnetohydrodynamic smhd equations in one and two space dimensions these equations model the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two dimensional with magnetic equilibrium in the third direction in this article we are using a variant of the ce se method developed by zhang et al a space time conservation element and solution element method for solving the two dimensional unsteady euler equations using quadrilateral and hexahedral meshes j comput phys 175 2002 168 199 this method uses structured and unstructured quadrilateral and hexahedral meshes in two and three space dimensions respectively in this method a single conservation element at each grid point is employed for solving conservation laws no matter in one two and three space dimensions the present scheme use the conservation element to calculate flow variables only while the gradients of flow variables are calculated by central differencing reconstruction procedure we give both one and two dimensional test computations a qualitative comparison reveals an excellent agreement with previous published results of wave propagation method and evolution galerkin schemes the one and two dimensional computations reported in this paper demonstrate the remarkable versatility of the present ce se scheme

a generalized neural network for solving a class of minimax optimization problems with linear constraints abstract in this paper a generalized neural network was proposed based on projection method and differential inclusions which is contributed to solve a class of minimax optimization problems with linear constraints it is proved that the solution trajectory can converge to the feasible region in the finite time when the initial point is not in the feasible region once the solution trajectory reaches the feasible region it will stay therein thereafter in addition we investigate the global convergence and exponential convergence furthermore three illustrative examples are given to show the efficiency of the proposed neural network

a space time conservation element and solution element method for solving the two and three dimensional unsteady euler equations using quadrilateral and hexahedral meshes in this paper we report a version of the space time conservation element and solution element ce se method in which the 2d and 3d unsteady euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes respectively in the present method mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for at each mesh point the value of a flow variable is obtained by imposing a flux conservation condition on the other hand the spatial derivatives are evaluated using a finite difference weighted average procedure note that the present extension retains many key advantages of the original ce se method which uses triangular and tetrahedral meshes respectively for its 2d and 3d applications these advantages include efficient parallel computing ease of implementing nonreflecting boundary conditions high fidelity resolution of shocks and waves and a genuinely multidimensional formulation without the need to use a dimensional splitting approach in particular because riemann solvers the cornerstones of the godunov type upwind schemes are not needed to capture shocks the computational logic of the present method is considerably simpler to demonstrate the capability of the present method numerical results are presented for several benchmark problems including oblique shock reflection supersonic flow over a wedge and a 3d detonation flow

transport of pollutant in shallow flows a space time ce se scheme abstract this paper focuses on implementation of space time ce se scheme for computing the transport of a passive pollutant by a flow the flow model comprises of the saint venant system of shallow water equations and the pollutant propagation is described by a transport equation the one dimensional and two dimensional flow equations are numerically investigated using the ce se scheme a number of test problems are presented to check the accuracy and efficiency of the proposed scheme the results of ce se scheme are compared with the central scheme both the schemes are found to be in close agreement however our proposed ce se scheme accurately captures shocks and discontinuous profiles

an algorithm for the inequality constrained discrete min max problem in this paper we discuss an approach using an augmented lagrangian formulation to directly solve the inequality constrained min max problem the algorithm involves a sequential quadratic programming subproblem an adaptive penalty parameter selection rule and a stepsize strategy convergent to unit steps that ensures progress toward optimality and feasibility of the inequality constraints it is shown that the penalty parameter does not grow indefinitely the convergence of the algorithm is established and its numerical effectiveness is demonstrated with test examples

a nonlinear augmented lagrangian for constrained minimax problems abstract a novel smooth nonlinear augmented lagrangian for solving minimax problems with inequality constraints is proposed in this paper which has the positive properties that the classical lagrangian and the penalty function fail to possess the corresponding algorithm mainly consists of minimizing the nonlinear augmented lagrangian function and updating the lagrange multipliers and controlling parameter it is demonstrated that the algorithm converges q superlinearly when the controlling parameter is less than a threshold under the mild conditions furthermore the condition number of the hessian of the nonlinear augmented lagrangian function is studied which is very important for the efficiency of the algorithm the theoretical results are validated further by the preliminary numerical experiments for several testing problems reported at last which show that the nonlinear augmented lagrangian is promising

a superlinearly convergent norm relaxed method of quasi strongly sub feasible direction for inequality constrained minimax problems in this paper nonlinear minimax problems with inequality constraints are discussed combined the norm relaxed sqp method with the idea of strongly sub feasible directions method a new method of quasi strongly sub feasible directions mqssfd with arbitrary initial point for the discussed problems is presented at each iteration of the proposed algorithm an improved search direction is obtained by solving a quadratic program qp which always has a solution and a high order correction direction is yielded via a system of linear equations sle to avoid the maratos effect after finite iterations the iteration point always get into the feasible set by introducing a new non monotone curve search under some mild conditions including the weak mangasarian fromovitz constraint qualification mfcq the proposed algorithm possesses global convergence and the superlinear convergence is obtained without the strict complementarity finally some elementary numerical experiments are implemented and reported

on the transition from regular to chaotic behaviour in the duffing oscillator a numerical procedure is introduced to study the transition from regular periodic motion to chaotic behaviour in the duffing oscillator having a soft characteristics this method is based on the computation of very accurate high order approximate periodic solutions of galerkin s type in conjunction with the corresponding stability analysis which is performed by computing the eigenvalues of a certain matrix related to the first variational equations the results obtained by this numerical method are in good agreement with those found previously by huberman and crutchfield who used an analog computer to obtain the phase portraits

an sqp feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity in this paper a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed and a new sqp feasible descent algorithm for solving the problems is presented at each iteration of the new algorithm a convex quadratic program qp which always has feasible solution is solved and a master direction is obtained then an improved feasible descent direction is yielded by updating the master direction with an explicit formula and in order to avoid the maratos effect a height order correction direction is computed by another explicit formula of the master direction and the improved direction the new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity furthermore the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted finally some numerical tests are reported

period doubling solutions in the duffing oscillator a galerkin approach the period doubling solutions for the attractor introduced by huberman and crutchfield are studied in the relevant range for the forcing frequency by a numerical method based on the computation of galerkin fourier approximations with very high accuracy for answering in an affirmative manner the questions of the existence of an exact period doubled solution the error estimate and the transition from a stable to an unstable solution very precise solutions combined with periodic series representations are required it is shown that the algorithm which uses galerkin fourier approximations of high order is a very efficient one

poincare maps of duffing type oscillators and their reduction to circle maps ii methods and numerical results bifurcation diagrams and plots of lyapunov exponents in the r plane for duffing type oscillators exhibit a regular pattern of repeating self similar tongues with complex internal structure we demonstrate here how this behaviour is easily understood qualitatively and quantitatively from a poincare map of the system in action angle variables in the limit of large driving force or equivalently small driving frequency this map approaches the one dimensional form as derived in paper i this second paper describes our approach to calculating the various constants and functions introduced in paper i it gives numerical applications of the theory and tests its range of validity by comparison with results from the numerical integration of duffing type equations finally we show how to extend the range in the parameter space where the map is applicable

gpu accelerated cese method for 1d shock tube problems in the present study a gpu accelerated 1d space time cese method is developed and applied to shock tube problems with and without condensation we have demonstrated how to implement the cese algorithm to solve 1d shock tube problems using an older generation gpu the nvidia 9800 gt with relatively limited memory to optimize the code performance we used shared memory and solved the inter block boundary problem in two ways namely the branch scheme and the overlapping scheme the implementations of these schemes are discussed in detail and their performances are compared for the sod shock tube problems for the sod problem without condensation the speedup over an intel cpu e7300 is 23 for the branch scheme and 41 for the overlapping scheme respectively while for problems with condensation both schemes achieve higher acceleration ratios 53 and 71 respectively the higher speedup of the condensation case can be ascribed to the source term calculation which has a local dependence on the mesh point and the source kernel has a higher acceleration ratio

a generalization of the norm relaxed method of feasible directions this paper generalizes the norm relaxed method of feasible directions which has roots in the classical method of feasible directions mfd this generalized algorithm introduces some parameters which can be adjusted to speed up the convergence an investigation of its global convergence is included and the numerical performance is shown on 15 test problems its global convergence is guaranteed under a rather mild and standard assumption the numerical tests show that this new algorithm converges faster than the previous norm relaxed mfd for most test problems by selecting a set of suitable parameters even though it only has the same guaranteed convergence rate as the previous norm relaxed mfd

aeroacoustic computations using a high order shock capturing scheme for aeroacoustic computations in the supersonic regime it is necessary to use a numerical scheme that can represent shock waves without generating spurious numerical oscillations the centered schemes that are usually used with success in the subsonic case combined with a selective filtering will generally oscillate in the presence of discontinuities a new class of shock capturing schemes the one step monotonicity preserving schemes combine the high accuracy and the nonoscillating property it is thus a good candidate for supersonic aeroacoustic applications the good spectral properties of these schemes are illustrated in the scalar linear case results of aeroacoustic test problems for the euler and navier stokes equations are compared with a dispersion relation preserving scheme the application to a supersonic cavity flow which induces a complex pattern of moving shocks shows that the one step monotonicity preserving schemes capture the moving discontinuities without spurious oscillations and preserve a high accuracy at the same time

doubling bifurcations of destroyed t 2 tori abstract two duffing oscillators driven with incommensurate frequencies and coupled additively are investigated with this system we observe a host of complex behavior which compete with each other in parameter space in particular the period doubling of an attracting t 2 torus and the destruction of a t 2 torus as the parameters are varied along a curve in parameter space we observe period doubling bifurcations of a destroyed t 2 torus this phenomenon is studied in greater detail via a simple recursive map

solving the mhd equations by the space time conservation element and solution element method we apply the space time conservation element and solution element cese method to solve the ideal mhd equations with special emphasis on satisfying the divergence free constraint of magnetic field i e b 0 in the setting of the cese method four approaches are employed i the original cese method without any additional treatment ii a simple corrector procedure to update the spatial derivatives of magnetic field b after each time marching step to enforce b 0 at all mesh nodes iii a constraint transport method by using a special staggered mesh to calculate magnetic field b and iv the projection method by solving a poisson solver after each time marching step to demonstrate the capabilities of these methods two benchmark mhd flows are calculated i a rotated one dimensional mhd shock tube problem and ii a mhd vortex problem the results show no differences between different approaches and all results compare favorably with previously reported data

a one step integration routine for normal differential systems based on gauss legendre quadrature abstract we introduce an integration procedure for normal differential systems implemented in pascal and based on a one step method using gauss legendre integration this procedure permits several levels of accuracy and determines an approximate solution of the differential system on an arbitrary user defined partition p n t 0 a t 1 t n 1 t n b t i 1 i i 1 n of a b r as well as an error estimation an interesting application for the method was provided by the study of the nature the stability and an accurate determination of the bifurcation points of the harmonic and subharmonic solutions of the forced duffing oscillator in order to show the onset of chaotic behaviour of the system for certain ranges of its forcing frequency

application of the space time conservation element and solution element method to one dimensional convection diffusion problems abstract in the space time conservation element and solution element ce se method the independent marching variables used comprise not only the mesh values of the physical dependent variables but also in contrast to a typical numerical method the mesh values of the spatial derivatives of these physical variables the use of the extra marching variables results from the need to construct the two level explicit and nondissipative schemes which are at the core of the ce se development it also results from the need to minimize the stencil while maintaining accuracy in this paper using the 1d a scheme as an example the effect of this added complication on consistency accuracy and operation count is assessed as part of this effort an equivalent yet more efficient form of the a scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced also the intriguing relations that exist among the a leapfrog and dufort frankel schemes are further explored in addition the redundancy of the leapfrog dufort frankel and lax schemes and the remedy for this redundancy are discussed this paper is concluded with the construction and evaluation of a ce se solver for the inviscid burgers equation

a robust algorithm for optimization with general equality and inequality constraints an algorithm for general nonlinearly constrained optimization is presented which solves an unconstrained piecewise quadratic subproblem and a quadratic programming subproblem at each iterate the algorithm is robust since it can circumvent the difficulties associated with the possible inconsistency of qp subproblem of the original sqp method moreover the algorithm can converge to a point which satisfies a certain first order necessary optimality condition even when the original problem is itself infeasible which is a feature of burke and han s methods math programming 43 1989 pp 277 303 unlike burke and han s methods our algorithm does not introduce additional bound constraints the algorithm solves the same subproblems as the han powell sqp algorithm at feasible points of the original problem under certain assumptions it is shown that the algorithm coincides with the han powell method when the iterates are sufficiently close to the solution some global convergence results are proved and locally superlinear convergence results are also obtained preliminary numerical results are reported

a simple feasible sqp method for inequality constrained optimization with global and superlinear convergence in this paper a simple feasible sqp method for nonlinear inequality constrained optimization is presented at each iteration we need to solve one qp subproblem only after solving a system of linear equations a new feasible descent direction is designed the maratos effect is avoided by using a high order corrected direction under some suitable conditions the global and superlinear convergence can be induced in the end numerical experiments show that the method in this paper is effective

derper an algorithm for the continuation of periodic solutions in ordinary differential equations abstract an algorithm for the continuation of periodic solutions of ode was derived and tested the algorithm is based on the shooting method and a standard continuation algorithm variational variables are used to compute the jacobi matrix the starting point on the periodic orbit is adaptively changed in the algorithm by fixing one component of the solution stability of periodic solutions along the continuous branch of solutions is determined by computing characteristic multipliers without difficulty the algorithm crosses limit points and at bifurcation points double period bifurcation points and points of tori bifurcation it proceeds along the original branch of solutions the usefulness of the algorithm is demonstrated in two examples one of them describes two stirred tank reactors with mutual mass exchange the other one is the lorenz model of turbulence

quadratically constraint quadratical algorithm model for nonlinear minimax problems abstract in this paper a quadratically approximate algorithm framework for solving general constrained minimax problems is presented the framework contains the idea of the sequential quadratic programming method the sequential quadratically constrained quadratic programming method norm relaxed method and strong sub feasible method the global convergence of the algorithm framework is obtained under the mangasarian fromovitz constraint qualification mfcq and the conditions for superlinear convergence of the algorithm framework are presented under the mfcq the constant rank constraint qualification crcq as well as the strong second order sufficiency conditions ssosc and quadratic convergence rate is obtained under the mfcq and ssosc

the space time cese scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients abstract the effects of bottom topography and horizontal temperature gradients on the shallow water flows are theoretically investigated the considered systems of partial differential equations pdes are non strictly hyperbolic and non conservative due to the presence of non conservative differential terms on the right hand side the solutions of these model equations are very challenging for a numerical scheme thus our primary goal is to introduce an improved numerical scheme which can handle the non conservative differential terms efficiently and accurately in this paper the space time conservation element and solution element cese method is extended to approximate these model equations the proposed scheme has capability to overcome all difficulties posed by this nonlinear system of pdes the performance of the scheme is analyzed by considering several case studies of practical interest and the results of suggested scheme are compared with those of central nt scheme the accuracy of the scheme is verified qualitatively and quantitatively

on chaos and fractal behavior in a generalized duffing s system abstract in this paper three duffing s equations their attractors and their initial condition maps are examined for elements of universality in the literature all three equations have been examined briefly before but their behavior has only been incompletely described this paper more completely examines these system and answers important questions concerning the reason for chaotic system behavior

feasible generalized monotone line search sqp algorithm for nonlinear minimax problems with inequality constraints in this paper the nonlinear minimax problems with inequality constraints are discussed and a sequential quadratic programming sqp algorithm with a generalized monotone line search is presented at each iteration a feasible direction of descent is obtained by solving a quadratic programming qp to avoid the maratos effect a high order correction direction is achieved by solving another qp as a result the proposed algorithm has global and superlinear convergence especially the global convergence is obtained under a weak mangasarian fromovitz constraint qualification mfcq instead of the linearly independent constraint qualification licq at last its numerical effectiveness is demonstrated with test examples