Recursos de colección
Lukashiv, Taras; Malyk, Igor
In this article the problem of existence and uniqueness of solutions of
stochastic differential equations with jumps and concentration points are
solved. The theoretical results are illustrated by one example.
Kohli, Ikjyot Singh; Haslam, Michael C.
We analyze, using a dynamical systems approach, the replicator dynamics for the
asymmetric Hawk-Dove game in which there is a set of four pure strategies with
arbitrary payoffs. We give a full account of the equilibrium points and their
stability and derive the Nash equilibria. We also give a detailed account of the
local bifurcations that the system exhibits based on choices of the typical
Hawk-Dove parameters $v$ and $c$ . We also give details on the connections between the results found in
this work and those of the standard two-strategy Hawk-Dove game. We conclude the
paper with some examples of numerical simulations that further illustrate some
global...
Misir, Adil; Mermerkaya, Banu
We compute explicitly the oscillation constant for Euler type half-linear
second-order differential equation having multi-different periodic
coefficients.
Katta, Ravinder; Sukavanam, N.
For an approximately controllable semilinear system, the problem of computing
control for a given target state is converted into an equivalent problem of
solving operator equation which is ill-posed. We exhibit a sequence of
regularized controls which steers the semilinear control system from an
arbitrary initial state ${x}^{\mathrm{0}}$ to an $\mathrm{ϵ}$ neighbourhood of the target state ${x}_{\tau }$ at time $\tau >\mathrm{0}$ under the assumption that the nonlinear function $f$ is Lipschitz continuous. The convergence of the sequences of regularized
controls and the corresponding mild solutions are shown under some assumptions
on the system operators. It is also proved that the target state corresponding
to the regularized...
Cengizci, Süleyman
In this work, approximations to the solutions of singularly perturbed
second-order linear delay differential equations are studied. We firstly use
two-term Taylor series expansion for the delayed convection term and obtain a
singularly perturbed ordinary differential equation (ODE). Later, an efficient
and simple asymptotic method so called Successive Complementary Expansion Method
(SCEM) is employed to obtain a uniformly valid approximation to this
corresponding singularly perturbed ODE. As the final step, we employ a numerical
procedure to solve the resulting equations that come from SCEM procedure. In
order to show efficiency of this numerical-asymptotic hybrid method, we compare
the results with exact solutions if possible; if not we compare with...
Singh, Brajesh Kumar; Kumar, Pramod
This paper deals with an alternative approximate analytic solution to
time fractional partial differential equations (TFPDEs) with
proportional delay, obtained by using fractional variational iteration
method, where the fractional derivative is taken in Caputo sense. The
proposed series solutions are found to converge to exact solution
rapidly. To confirm the efficiency and validity of FRDTM, the
computation of three test problems of TFPDEs with proportional delay
was presented. The scheme seems to be very reliable, effective, and
efficient powerful technique for solving various types of physical
models arising in science and engineering.
Su, Cheng-Min; Sun, Jian-Ping; Zhao, Ya-Hong
In this paper, we study the existence and uniqueness of solutions for the
following boundary value problem of nonlinear fractional differential equation:
$({}^{C}{D}_{\mathrm{0}+}^{q}u)(t)=f(t,u(t))$ , $t\in (\mathrm{0,1})$ , $u(\mathrm{0})={u}^{\mathrm{\prime }\mathrm{\prime }}(\mathrm{0})=\mathrm{0}, ({}^{C}{D}_{\mathrm{0}+}^{{\sigma }_{\mathrm{1}}}u)(\mathrm{1})=\lambda ({I}_{\mathrm{0}+}^{{\sigma }_{\mathrm{2}}}u)(\mathrm{1})$ , where $\mathrm{2}\mathrm{0}$ , and $\lambda \ne \mathrm{\Gamma }(\mathrm{2}+{\sigma }_{\mathrm{2}})/\mathrm{\Gamma }(\mathrm{2}-{\sigma }_{\mathrm{1}})$ . The main tools used are nonlinear alternative of Leray-Schauder type
and Banach contraction principle.
Bernal-Vílchis, Fernando; Hayashi, Nakao; Naumkin, Pavel I.
We consider the Cauchy problem for the Ostrovsky-Hunter equation ${\partial }_{x}({\partial }_{t}u-(b/\mathrm{3}){\partial }_{x}^{\mathrm{3}}u-{\partial }_{x}\mathcal{K}{u}^{\mathrm{3}})=au$ , $(t,x)\in {\mathbb{R}}^{\mathrm{2}}$ , $u(\mathrm{0},x)={u}_{\mathrm{0}}(x)$ , $x\in \mathbb{R}$ , where $ab>\mathrm{0}$ . Define ${\xi }_{\mathrm{0}}={(\mathrm{27}a/b)}^{\mathrm{1}/\mathrm{4}}$ . Suppose that $\mathcal{K}$ is a pseudodifferential operator with a symbol $\stackrel{^}{K}(\xi )$ such that $\stackrel{^}{K}(\pm{\xi }_{\mathrm{0}})=\mathrm{0}$ , $\mathrm{I}\mathrm{m} \stackrel{^}{K}(\xi )=\mathrm{0}$ , and $|\stackrel{^}{K}(\xi )|\le C$ . For example, we can take $\stackrel{^}{K}(\xi )=({\xi }^{\mathrm{2}}-{\xi }_{\mathrm{0}}^{\mathrm{2}})/({\xi }^{\mathrm{2}}+\mathrm{1})$ . We prove the global in time existence and the large time asymptotic
behavior of solutions.
Ngwane, F. F.; Jator, S. N.
In this paper, we present a block hybrid trigonometrically fitted
Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of
the frequency and the step-size for directly solving general second-order
initial value problems (IVPs), including Hamiltonian systems such as the energy
conserving equations and systems arising from the semidiscretization of partial
differential equations (PDEs). Four discrete hybrid formulas used to formulate
the BHTRKNM are provided by a continuous one-step hybrid trigonometrically
fitted method with an off-grid point. We implement BHTRKNM in a block-by-block
fashion; in this way, the method does not suffer from the disadvantages of
requiring starting values and predictors which are inherent in
predictor-corrector methods. The stability property of the...
Biala, T. A.; Jator, S. N.
A family of boundary value methods (BVMs) with continuous coefficients is derived
and used to obtain methods which are applied via the block unification approach.
The methods obtained from these continuous BVMs are weighted the same and are
used to simultaneously generate approximations to the exact solution of systems
of second-order boundary value problems (BVPs) on the entire interval of
integration. The convergence of the methods is analyzed. Numerical experiments
were performed to show efficiency and accuracy advantages.
Djiomba Njankou, Sylvie Diane; Nyabadza, Farai
A six-compartment mathematical model is formulated to investigate the role of
media campaigns in Ebola transmission dynamics. The model includes tweets or
messages sent by individuals in different compartments. The media campaigns
reproduction number is computed and used to discuss the stability of the disease
states. The presence of a backward bifurcation as well as a forward bifurcation
is shown together with the existence and local stability of the endemic
equilibrium. Results show that messages sent through media have a more
significant beneficial effect on the reduction of Ebola cases if they are more
effective and spaced out.