An integral-equation function-space method for solving inequality-constrained optimal control problems†

A function-space method using an integral equation representation of the second variation is applied to inequality-constrained optimal control problems. Numerical solutions for a bang-bang control problem and a singular control problem are solved using the computational algorithm.     

Teaching–Learning-Based Optimization: An optimization method for continuous non-linear large scale problems

An efficient optimization method called ‘Teaching–Learning-Based Optimization (TLBO)’ is proposed in this paper for large scale non-linear optimization problems for finding the global solutions. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The effectiveness of the method is tested on many benchmark problems with different characteristics and the results are compared with other population based methods.     

An assessment of the Padé-Laplace method for transient electric birefringence decay analysis

We implemented and tested the Padé-Laplace method for analyzing a sum of exponential decays, and applied it to transient electric birefringence decay measurements on DNA samples. The Padé-Laplace method involves integrating the decay data to calculate the Taylor expansion of the Laplace transform. The Padé approximant of the Laplace transform can be calculated from the Taylor series, and is then used to determine the number and value of the time constants in the decay. False solutions with complex and positive (diverging) exponentials were obtained from data but these false solutions were easily discarded. We found the method to be remarkably robust to random noise, but very sensitive to baseline errors. The same data sets were analyzed using the well-established deconvolution program CONTIN. The Padé-Laplace method could resolve time constants better than CONTIN from noisy data, but CONTIN compensated for baseline errors much more effectively. The time for executing either analysis on a microcomputer was almost the same.     

Third-order composite Runge–Kutta method for stiff problems

The derivation of a composite method for solving stiff ordinary differential equations is discussed. Combination of the harmonic and arithmetic means of the Runge–Kutta formulation has resulted in the introduction of a new formula for the numerical solution of stiff ordinary differential equations. The numerical results and the A-stability of this new formula are examined.     

A Guass–Newton-like method for inverse eigenvalue problems

In this paper, we propose a Guass–Newton-like method for finding least-square solutions to inverse eigenvalue problems. We show that the proposed method converges under some mild conditions. In particular, if the method converges to the exact solution, the convergence rate is at least quadratic in the root sense. Numerical examples are given to justify the theoretical result.     

An ϵ-uniform fitted operator method for solving boundary-value problems for singularly perturbed delay differential equations: Layer behavior

In this paper, an ?-uniform fitted operator method which solves boundary-value problems for singularly perturbed differential-difference equations containing small delay with boundary layer behavior is presented. Both the cases, i.e., when boundary layer is on the left side and when boundary layer is on the right side are discussed here. It is shown that the scheme is ?-uniform by establishing the error estimate. The effect of small delay on the boundary layer solution is shown by considering several numerical experiments. Numerical results in terms of maximum errors are tabulated and plots giving computed and exact solution demonstrate the efficiency of the method.     

“Booster method” for singularly perturbed robin problems i

An improved numerical method is presented for singularly perturbed Robin problems in this paper. In this method (“Booster method”), an asymptotic approximation is incorporated into a finite difference scheme to improve the numerical solution. Error estimates are proposed for the present method. In order to show the efficiency numerical examples are presented.     

An algebraic method for control systems design†

A computer-oriented algebraic method for the design of duplicator class control systems is established. To involves four steps: (1) Equation fitting, (2) parameter assuming, (3) system simplifying and (4) quotient matching. The power and simplicity of the method are demonstrated by several examples.     

On a modified Numerov's method for inverse Sturm–Liouville problems

In this paper, we discuss the convergence of modified Numerov's method in Q. Gao, X.L. Cheng and Z.D. Huang [Modified Numerov's method for inverse Sturm–Liouville problems, J. Comput. Appl. Math. 253 (2013), pp. 181–199] for computing symmetric potentials from finite Dirichlet eigenvalues. A sufficient condition for convergence of the estimate to the true potential is given and the rate of convergence is investigated. The proof relies on the asymptotics of eigenvalues of the Sturm–Liouville operator and the errors in the finite difference eigenvalues obtained by Numerov's approach. Some numerical experiments are presented to confirm the theoretically predicted convergence properties.     

A computational method for parameter optimization problems arising in control†

A parameter optimization procedure is presented for large-scale problems arising in linear control system design that include equality and inequality constraints. The procedure is based on a novel min—max algorithm for locating a constrained relative minimum without the use of penalty functions or slack variables. This algorithm is constructed from an auxiliary minimization problem with equality constraints. Inequality constraints then are introduced using the notion of an effective constraint. Typical problem formulations are discussed, and an extensive design example is presented.     

An assessment of discretizations for convection-dominated convection–diffusion equations

The performance of several numerical schemes for discretizing convection-dominated convection–diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov–Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.     

An integrated AHP–DEA methodology for bridge risk assessment

The traditional analytic hierarchy process (AHP) method can only compare a very limited number of decision alternatives, which is usually not more than 15. When there are hundreds or thousands of alternatives to be compared, the pairwise comparison manner provided by the traditional AHP is obviously infeasible. In this paper we propose an integrated AHP–DEA methodology to evaluate bridge risks of hundreds or thousands of bridge structures, based on which the maintenance priorities of the bridge structures can be decided. The proposed AHP–DEA methodology uses the AHP to determine the weights of criteria, linguistic terms such as High, Medium, Low and None to assess bridge risks under each criterion, the data envelopment analysis (DEA) method to determine the values of the linguistic terms, and the simple additive weighting (SAW) method to aggregate bridge risks under different criteria into an overall risk score for each bridge structure. The integrated AHP–DEA methodology is applicable to any number of decision alternatives and is illustrated with a numerical example.     

The singular-G method for unstable non-minimum-phase plants†

In linear time-invariant feedback systems with plants which have both poles and zeros in the right half-plane, it is always possible to stabilize the system for a fixed plant. But in the previous optimum techniques, the stability margins might be so small as to render the design wholly impractical. This problem was overcome in the X-29 aircraft in a multiple-input-multiple-output (MIMO) setting, by use of a singular-G (compensation) matrix inside the loop. Excellent stability margins were then achievable over a wide plant parameter range, by means of a fixed-G compensation matrix.

This paper extends the singular-G technique to the single-input-single-output (SISO) plant. The latter is converted into an equivalent N × N MIMO plant by means of N parallel independent time-varying modulators acting on the plant output, a technique previously used for non-linear network synthesis. The singular-G method is then applicable to the equivalent N × N MIMO plant. The detailed design procedure is presented by means of an example with N = 2.     

The Philosophy of Critical Realism—An Opportunity for Information Systems Research

It is argued that recent research in the information systems field has tended to either emphasise the structural/collective dimension or the agency/individual dimension, not both. Structuration theory is a more recent attempt to address both agency and structure, however there are a number of issues with the use of structuration theory in information systems research, not the least of which is its lack of recognition of the temporal and longitudinal nature of information systems development. A relatively new philosophy, critical realism, provides the potential for a new approach to social investigations in its provision of an ontology for the analytical separation of structure and agency. The philosophy is introduced and its implications for sociological investigation are discussed.     

Smoothing projected cyclic Barzilai–Borwein method for stochastic linear complementarity problems

In this paper, we propose a smoothing projected cyclic Barzilai–Borwein (SPCBB) method for solving the expected residual minimization formulation of stochastic linear complementarity problems (SLCPs). The SPCBB method combines the smoothing techniques and the projected Barzilai–Borwein (BB) method, where the cyclic BB scheme which resues the same BB stepsize for several consecutive iterations and a nonmonotone line search that requires an average of the successive function values decreases are employed to accelerate the convergence process. Under mild conditions, we show the convergence of the proposed method to a Clarke stationary point. Preliminary numerical results of randomly generated SLCPs show that the method is promising.     

A parameter-free dynamic diffusion method for advection–diffusion–reaction problems

In this paper, we present a two-scale finite element formulation, named Dynamic Diffusion (DD), for advection–diffusion–reaction problems. By decomposing the velocity field in coarse and subgrid scales, the latter is used to determine the smallest amount of artificial diffusion to minimize the coarse-scale kinetic energy. This is done locally and dynamically, by imposing some constraints on the resolved scale solution, yielding a parameter-free consistent method. The subgrid scale space is defined by using bubble functions, whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. Convergence tests on a two-dimensional example are reported, yielding optimal rates. In addition, numerical experiments show that DD method is robust for a wide scope of application problems.     

A modified Sobol′ sensitivity analysis method for decision-making in environmental problems

Sensitivity analysis is an important component of environmental modelling and in recent years, variance-based, global sensitivity analysis techniques, such as Sobol′, have been a preferred approach for achieving this. However, these techniques are generally only applicable to simulation models and not to models used to rank alternative options, such as multi-criteria decision analysis (MCDA) methods. In order to overcome this limitation, a modified Sobol′ method for MCDA (Sobol′-MCDA) is introduced in this paper. The method has the following features: (i) it enables the stability or robustness of the relative ranking of two alternatives to be assessed in the light of changes in assessment criteria and stakeholder preferences; and (ii) it enables the sensitivity of the ranking of two alternatives to changes in assessment criteria and stakeholder preferences to be assessed. The approach is demonstrated for a water resources case study from the literature consisting of seven alternatives and ten assessment criteria.     

Prüfer method for periodic and semi-periodic sturm-liouville eigenvalue problems ∗

In reference [19], the authors developed a shooting algorithm for Sturm-Liouville eigenvalue problems associated with periodic and semi-periodic boundary conditions. The technique is based on the application of the Floquet theory, and it has proven to be efficient for computing eigenvalues. However, the performance of this technique depends upon the choice of the starting eigenvalues. In the present paper, we continue our study and employ the Prüfer method. An attractive property of this method is that eigenvalues can usually be accurately computed even when no information on the eigenvalue distribution is provided. Sufficient conditions for convergence, error bounds and a procedure to improve the stability are discussed. Some numerical examples are given to illustrate the effectiveness of the proposed method.     

A stable space–time finite element method for parabolic evolution problems

This paper is concerned with the analysis of a new stable space–time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on the FEM space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the FEM spaces yield an a priori discretization error estimate with respect to the discrete norm. Finally, we confirm the theoretical results with numerical experiments in spatial moving domains.