In this paper, the optimal homotopy asymptotic method (OHAM) is applied to obtain an approximate solution of the nonlinear Riccati differential equation. The method is tested on several types of Riccati differential equations and comparisons that were made with numerical results showed the effectiveness and accuracy of this method.
In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the Cauchy reaction-diffusion problems. HPM yields solutions in convergent series forms with easily computable terms. The HPM is tested for several examples. Comparisons of the results obtained by the HPM with that obtained by the Adomian decomposition method (ADM), homotopy analysis method (HAM) and the exact solutions show the efficiency of HPM.
In this paper, we investigate the dynamical behavior in an M-dimensional nonlinear hyperchaotic model (M-NHM), where the occurrence of multistability can be observed. Four types of coexisting attractors including single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors can be found, which are unusual behaviors in discrete chaotic systems. Furthermore, the coexistence of asymmetric and symmetric properties can be distinguished for a given set of parameters. In the endeavor of chaotification, this work introduces a simple controller on the M-NHM, which can add one more loop in each iteration, to overcome the chaos degradation in the multistability regions.
In this paper, systems of second-order boundary value problems (BVPs) are considered. The applicability of the homotopy-perturbation method (HPM) was extended to obtain exact solutions of the BVPs directly.
A map on a group is not necessarily an automorphism on the group. In this paper we determined the necessary and sufficient conditions of a map on a split metacyclic p-group to be an automorphism, where we only considered p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We considered the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then used the relations and the regularity of the split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism.
n this paper, transformation and differentiation of Henstock-Wiener integrals are discussed. The approach is by Riemann sums. The idea is more transparent than that of classical Wiener integral.
In this paper, we study the effects of symmetrization by the implicit midpoint rule (IMR) and the implicit trapezoidal rule
(ITR) on the numerical solution of ordinary differential equations. We extend the study of the well-known formula of Gragg
to a two-step symmetrizer and compare the efficiency of their use with the IMR and ITR. We present the experimental results
on nonlinear problem using variable stepsize setting and the results show greater efficiency of the two-step symmetrizers
over the one-step symmetrizers of IMR and ITR.
A map on a group is not necessarily an automorphism on the group. In this paper we study the necessary and sufficient conditions for a map on a non-split metacyclic p-group to be an automorphism, where we only consider p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We consider the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then use the relations and the regularity of the non-split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism.
Special Protection Schemes (SPSs), are corrective action schemes that are designed to protect power
systems against severe contingency conditions. In planning of SPSs, protecting transmission network from
overloading issue due to critical situations has become a serious challenge which needs to be taken into
account. In this paper, a Special Protection and Control Scheme (SPCS) based on Differential Evolution
(DE) algorithm for optimal generation rescheduling has been applied to mitigate the transmission line
overloading in system contingency conditions. The N-1 contingency has been performed for different
single line outages under base and increased load in which generation rescheduling strategy has been
undertaken to overcome the overloading problem. Simulation results are presented for both pre-and
post system emergency situations. The IEEE 30-bus test system was utilised in order to validate the
effectiveness of the proposed method.
In this paper, we consider the system of Volterra-Fredholm integral equations
of the second kind (SVFI-2). We proposed fixed point method (FPM) to solve
SVFI-2 and improved fixed point method (IFPM) for solving the problem. In addition,
a few theorems and two new algorithms are introduced. They are supported by
numerical examples and simulations using Matlab. The results are reasonably good
when compared with the exact solutions.
In this paper a class of capital investment problem is considered within the context of mathematical programming. The usual and commonly used approach is presented upon the basis of the next present value criterion, and a branch and bound method is discussed for a model under extended assumptions.
Dalam kertas ini satu kelas masalah pelaburan kapital difikirkan di dalam konteks pengaturcaraan matematik. Pendekatan biasa dan selalu digunakan, dikemukakan berasaskan kriterium Nilai Semasa Berikut dan satu kaedah bercabang dan terbatas dibincangkan untuk satu model di bawah anggapan yang diperluaskan.