Showing papers in "Journal of Computational and Applied Mathematics in 2006"

TL;DR: This paper investigates the computational aspects of the Galerkin approximation using continuous piecewise polynomial basis functions on a regular triangulation of the domain and demonstrates approximations to FADEs.

TL;DR: Adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations: Dxiyi(x) = Ni(x, y1,...,yn), yi(k)(0) = cki, 0 ≤k ≤[αi], 1≤i≤n and Dxi denotes Caputo fractional derivative as mentioned in this paper.

TL;DR: In this paper, the existence, uniqueness, and global exponential stability of equilibrium point for Cohen-Grossberg neural networks with both time-varying and continuously distributed delays is considered.

TL;DR: In this article, a prey-predator model incorporating a predator-refuge and independent harvesting in either species was considered and the problem of optimal harvest policy was solved by using Pontryagin's maximal principle.

TL;DR: In this paper, a critical comparison of the suitability of several numerical methods, level set, moving grid and phase field model, to address two well-known Stefan problems in phase transformation studies is presented.

TL;DR: This paper proposes a method based on Bezier nets to calculate the dimension of a spline function space over a T-mesh and obtains the dimension formulae for T-meshes after mesh operations, such as edge insertion and mesh merging.

TL;DR: Numerical tests show that an automated approach to adjusting the learning parameters using a derivative-free numerical optimizer can produce support vector machines that are very well tuned to their classification tasks.

TL;DR: In this paper, the Adomian decomposition method is applied to solve both linear and nonlinear boundary value problems (BVPs) for fourth-order integro-differential equations.

TL;DR: In this article, the problem of implementing fast algorithms for the numerical solution of initial value problems of the form x(α)(t) = f(t, x(t)), x(0) = x0, where X(α) is the derivative of x of order α in the sense of Caputo and 0 < α < 1.

TL;DR: In this paper, an algorithm for solving nonlinear monotone equations is proposed, which combines a modified spectral gradient method and projection method, and it is shown to be globally convergent to a solution of the system if the nonlinear equations to be solved is Monotone and Lipschitz continuous.

TL;DR: In this article, the authors investigated the dynamic behavior of a Holling II functional response predator-prey system concerning impulsive control strategy-periodic releasing natural enemies and spraying pesticide at different fixed times.

TL;DR: In this paper, the regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method and the same method is applied to the time-split RLW equation.

TL;DR: In this article, the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes were investigated, and it was shown that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability.

TL;DR: In this article, sufficient conditions for oscillation of the second-order nonlinear neutral delay dynamic equation on a time scale T are established; here γ ≥ 1 is an odd positive integer with r(t) and p(t), are rd-continuous functions defined on T.

TL;DR: A class of explicit two-step hybrid methods for the numerical solution of second-order IVPs which reach up to order five and six with only three and four stages per step, respectively, and which have optimized the error constants.

TL;DR: In this article, it is shown how a Gauss-Newton method in the rotation parameters alone can easily be implemented to determine the parameters of the nine-parameter transformation (when different scale factors for the variables are needed).

TL;DR: In this paper, a pseudospectral solution of Fisher's equation is developed, which is characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient.

TL;DR: This paper reports new progress on the robust conforming and constrained boundary recovery in three dimensions, along with the quality mesh generation based on Centroidal Voronoi tessellations.

TL;DR: In this paper, a non-local PDE model for the evolution of a single species population that involves delayed feedback is proposed, where the delay such as the maturation time in the delayed birth rate, is selective and the selection depends on the status of the system.

TL;DR: This paper develops a procedure to obtain k-step Falkner methods (explicit and implicit) in their variable step-size versions, providing recurrence formulas to compute the coefficients efficiently.

TL;DR: In this paper, positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative features as the corresponding continuous predator-prey models, are formulated and analyzed.

TL;DR: By solving an infinite nonlinear system of q-difference equations one constructs a chain of qdifference operators, and some applications, including the one related to q-Hahn orthogonal polynomials, are discussed.

TL;DR: In this article, the existence theorem of periodic solution of order one for a general planar autonomous impulsive system with state-dependent impulsion has been proved for a special case of the problem, and the concrete conditions of existence of one-order periodic solution for that special system have been obtained.

TL;DR: In this paper, an inverse problem of reconstructing the coefficient q in the parabolic equation from the final measurement u(x, T), where q is in some subset of L1(Ω) was considered.

TL;DR: In this article, a quadratic Lyapunov function with a common matrix is used to derive a stabilizing switching control strategy that guarantees: (i) the assignment of all the eigenvalues of each linear subsystem inside a chosen circle in the left-hand half of the complex plane; (ii) a minimum disturbance attenuation level for the closed-loop switched system.

TL;DR: In this paper, the authors presented some down-to-earth calculations in this context, and solved the problem by modeling the income process of the company by a Wiener process and imposing the condition of a bounded dividend rate.

TL;DR: A type of single-hidden layer feedforward neural networks with sigmoidal nondecreasing activation function that can uniformly approximate any continuous function of one variable and can be used for constructing uniform approximants of continuous functions of several variables is presented.

TL;DR: In this article, a modification of the double projection algorithm for solving variational inequalities is presented, where the main modification is to use a different Armijo-type linesearch to obtain a hyperplane strictly separating current iterate from the solutions of the variational inequality.

TL;DR: This paper presents an efficient symbolic-numerical approach for generating and solving the boundary value problem-differential algebraic equation (BVP-DAE) originating from the variational form of the optimal control problem (OCP).

TL;DR: Numerical results show that these restrictive preconditioners can lead to practical and effective PCG methods for solving large sparse systems of linear equations of symmetric positive definite and block two-by-two coefficient matrices.