Journal of Applied Mathematics and Computing
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A local-global stepsize control for multistep methods applied to semi-explicit index 1 differential-algebraic equations
Journal of Applied Mathematics and Computing - - 1999
Enhanced shifted Tchebyshev operational matrix of derivatives: two spectral algorithms for solving even-order BVPs
Journal of Applied Mathematics and Computing - Tập 69 - Trang 3893-3909 - 2023
Herein, new orthogonal polynomials have been generated from shifted Chebyshev polynomials that fulfill a given set of homogeneous boundary conditions and the necessary formulae have been established. Moreover, an integer order derivative operational matrix has been introduced. Then, the presented novel polynomials are used together with the two spectral methods, namely, the Galerkin and Tau method......
Existence and global exponential stability of almost periodic solution for CNNs with variable coefficients and delays
Journal of Applied Mathematics and Computing - Tập 28 - Trang 461-472 - 2008
By using exponential dichotomy and the Banach fixed-point theory and combining Yang inequality, some sufficient conditions are derived ensuring existence and global exponential stability of almost periodic solution for CNNs with variable coefficients and delays. Without assuming the boundedness of signal function, these results obtained here can be expected to have highly important significance in......
The anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation
Journal of Applied Mathematics and Computing - Tập 27 - Trang 97-106 - 2008
This paper discusses the anti-symmetric ortho-symmetric solution of a linear matrix equation and its optimal approximation. By the generalized singular value decomposition of the matrices, the necessary and sufficient conditions for the solvability of the matrix equation and the general form of the anti-symmetric ortho-symmetric solution are given. In addition, the existence and uniqueness of the ......
A family of the modified three-term Hestenes–Stiefel conjugate gradient method with sufficient descent and conjugacy conditions
Journal of Applied Mathematics and Computing - Tập 69 - Trang 2331-2360 - 2023
To strengthen the three-term Hestenes–Stiefel conjugate gradient method proposed by Zhang et al., we suggest a modified version of it. For this purpose, by considering the Dai–Liao approach, the third term of Zhang et al. method is multiplied by a positive parameter which can be determined adaptively. To render an appropriate choice for the parameter of the search direction, we carry out a matrix ......
Dynamics of n+1-dimensional impulsive reaction-diffusion predator-prey system with Holling type III functional response
Journal of Applied Mathematics and Computing - Tập 45 - Trang 275-296 - 2013
An n+1-dimensional impulsive reaction-diffusion periodic predator-prey system with Holling type III functional response is investigated in the present paper. Sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established based on the comparison theory of differential equation and upper and lower solution method. By constructing appropriate auxiliary fu......
Periodic solutions of some autonomous second order Hamiltonian systems
Journal of Applied Mathematics and Computing - Tập 28 - Trang 51-58 - 2008
In this paper, we study the existence of periodic solutions of some autonomous second order Hamiltonian systems
$$\left\{\begin{array}{l}\ddot{u}(t)=\nabla{H(u(t)),}\\[3pt]u(0)-u(T)=\dot{u}{(0)}-\dot{u}{(T)}=0.\end{array}\right.$$
We obtain some new existence theorems by the least action principle.
Multiplicity of positive solutions for a nonlinear m-point BVP with sign changing nonlinearity on time scales
Journal of Applied Mathematics and Computing - Tập 34 - Trang 163-175 - 2009
In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for a nonlinear m-point boundary value problem for the following second-order dynamic equation on time scales
$$\begin{array}{l}(\phi(u^{\Delta}))^{\nabla}+a(t)f(t,u(t))=0,\quad t\in(0,T),\\\noalign{\vspace{2mm}}\dis......
Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup
Journal of Applied Mathematics and Computing - Tập 32 - Trang 39-58 - 2009
This paper deals with the 〈N,p〉-policy M/G/1 queue with server breakdowns and general startup times, where customers arrive to demand the first essential service and some of them further demand a second optional service. Service times of the first essential service channel are assumed to follow a general distribution and that of the second optional service channel are another general distribution.......
Full-rank block LDL ∗ decomposition and the inverses of n×n block matrices
Journal of Applied Mathematics and Computing - Tập 40 - Trang 569-586 - 2012
Full-rank block LDL
∗ decomposition of a Hermitian n×n block matrix A is examined, where the iterative procedure evaluating the sub-matrices appearing in L and D is provided. This factorization is used to evaluate the inverse and Moore-Penrose inverse of a Hermitian n×n block matrix. The method for the calculation of the Moore-Penrose inverse of an arbitrary 2×2 block matrix is als......
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