]>
2018
11
12
ISSN 2008-1898
97
Timer option pricing of stochastic volatility model with changing coefficients under time-varying interest rate
Timer option pricing of stochastic volatility model with changing coefficients under time-varying interest rate
en
en
Considering economic variables changing from time to time, the time-varying models can fit the financial data better. In this paper, we construct stochastic volatility models with time-varying coefficients. Furthermore, the interest rate risk is one of important factors for timer options pricing. Therefore, we study the timer options pricing for stochastic volatility models with changing coefficients under time-varying interest rate. Firstly, the partial differential equation boundary value problem is given by using \(\Delta\)-hedging approach and replicating a timer option. Secondly, we obtain the joint distribution of the variance process and the random maturity under the risk neutral probability measure. Thirdly, the explicit formula of timer option pricing is proposed which can be applied to the financial market directly. Finally, numerical analysis is conducted to show the performance of timer option pricing proposed.
1294
1301
Jixia
Wang
Jixia
Wang
Henan Normal University
Henan Normal University
China
Dongyun
Zhang
Dongyun
Zhang
Henan Normal University
Henan Normal University
China
Timer option pricing
stochastic volatility model
risk neutral measure
\(\Delta\)-hedging
time-varying interest rate
timer-option-pricing-of-stochastic-volatility-model-with-changing-coefficients-under-time-varying-interest-rate.pdf
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C. Bernard, Z. Cui , Pricing Timer Options, J. Comput. Finance, 15 (2011), 69-104
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A. Bick , Quadratic-variation-based dynamic strategies , Manage. Sci., 41 (1995), 722-732
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M. Broadie, J. B. Detemple, Anniversary article: Option pricing: Valuation models and applications, Manage. Sci., 50 (2004), 1145-1177
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M. Broadie, A. Jain, Pricing and Hedging Volatility Derivatives, The Journal of Derivatives, 15 (2008), 7-24
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P. Carr, R. Lee, Hedging variance options on continuous semimartingales, Finance Stoch., 14 (2010), 179-207
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J. C. Cox, J. Ingersoll, E. Jonathan, S. A. Ross, A Theory of the Term Structure of Interest Rates, Econometrica, 53 (1985), 385-407
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R. Frey, C. A. Sin, Bounds on European Option Prices under Stochastic Volatility, Math. Finance, 9 (1999), 97-116
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S. L. Heston, A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Rev. Financ. Stud., 6 (1993), 327-343
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J. C. Hull, A. D. White, The pricing of options on Assets with Stochastic Volatilities, J. Finance, 42 (1998), 281-300
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C. Li, Bessel Process, Stochastic Volatility and Timer Options, Math. Finance, 26 (2016), 122-148
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M. Li, F. Mercurio, Closed Form Approximation of Timer Option Prices Under General Stochastic Volatility Models, University Library of Munich, 2013 (2013), 1-44
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A. J. Neuberger, Volatility Trading, Londan Business School, London (1990)
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D. Saunders, Pricing Timer Options Under Fast Mean-reverting Stochastic Volatility, Can. Appl. Math. Q., 17 (2009), 737-753
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S. E. Shreve , Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer-Verlag, New York (2004)
]
Numerical solution for a nonlinear obstacle problem
Numerical solution for a nonlinear obstacle problem
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en
A monotone iterations algorithm combined with the finite difference method is constructed for an obstacle
problem with semilinear elliptic partial differential equations of second order. By means of Dirac delta
function to improve the computation procedure of the
discretization, the finite difference method is still practicable even though the obstacle boundary is irregular. The numerical simulations show that our proposed methods are feasible and effective for the nonlinear obstacle problem.
1302
1312
Ling
Rao
Ling
Rao
Nanjing University of Science and Technology
Nanjing University of Science and Technology
China
Shih-Sen
Chang
Shih-Sen
Chang
China Medical University
China Medical University
Taiwan
Finite difference method
nonlinear obstacle problem
variational inequality
elliptic partial differential equation
numerical-solution-for-a-nonlinear-obstacle-problem.pdf
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D. Boffi, L. Gastaldi, A finite element approach for the immersed boundary method, Comput. Structures, 81 (2003), 491-501
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]
Traveling waves for a diffusive SIR model with delay and nonlinear incidence
Traveling waves for a diffusive SIR model with delay and nonlinear incidence
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en
This paper is concerned with the existence and non-existence of traveling wave solutions for a diffusive SIR model with delay and nonlinear incidence. First, we construct a pair of upper and lower solutions and a bounded cone. Then we prove the existence of traveling wave by using Schauder's fixed point theorem and constructing a suitable Lyapunov functional. The nonexistence of traveling wave is obtained by two-sided Laplace transform. Moreover, numerical simulations support the theoretical results. Finally, we also obtain that the minimal wave speed is decreasing with respect to the latent period and increasing with respect to the diffusion rate of infected individuals.
1313
1330
Yanmei
Wang
Yanmei
Wang
Shanxi University
Shanxi University of Finance and Economics
Shanxi University
Shanxi University of Finance and Economics
China
China
Guirong
Liu
Guirong
Liu
Shanxi University
Shanxi University
China
Aimin
Zhao
Aimin
Zhao
Shanxi University
Shanxi University
China
SIR model
traveling wave
time delay
nonlinear incidence
traveling-waves-for-a-diffusive-sir-model-with-delay-and-nonlinear-incidence.pdf
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Z. G. Bai, S.-L. Wu, Traveling waves in a delayed SIR epidemic model with nonlinear incidence, Appl. Math. Comput., 263 (2015), 221-232
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E. Beretta, T. Hara, W. Ma, Y. Takeuchi , Global asymptotic stability of an SIR epidemic model with distributed time delay , Nonlinear Anal., 47 (2001), 4107-4115
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J. Fang, J. J. Wei, X.-Q. Zhao, Spatial dynamics of a nonlocal and time-delayed reaction diffusion system, J. Differential Equations, 245 (2008), 2749-2770
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S.-C. Fu , Traveling waves for a diffusive SIR model with delay, J. Math. Anal. Appl., 435 (2016), 20-37
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G. Huang, Y. Takeuchi, W. Ma, D. Wei, Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate, Bull. Math. Biol., 72 (2010), 1192-1207
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A. Korobeinikov , Global properties of infectious disease models with nonlinear incidence, Bull. Math. Biol., 69 (2007), 1871-1886
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A. Korobeinikov , Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 68 (2006), 615-626
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A. Korobeinikov, P. K. Maini , Non-linear incidence and stability of infectious disease models, Math. Med. Biol., 22 (2005), 113-128
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W. Ma, Y. Takeuchi, T. Hara, E. Beretta, Permanence of an SIR epidemic model with distributed time delays, Tohoku Math. J., 54 (2002), 581-591
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S. G. Ruan, W. D. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differential Equations, 188 (2003), 135-163
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M. A. Safi, A. B. Gumel, The effect of incidence functions on the dynamics of a quarantine/isolation model with time delay, Nonlinear Anal. Real World Appl., 12 (2011), 215-235
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Y. Takeuchi, W. Ma, E. Beretta , Global asymptotic properties of a delay SIR epidemic model with finite incubation times, Nonlinear Anal. Ser. A: Theory Methods, 42 (2000), 931-947
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P. X. Weng, X.-Q. Zhao, Spreading speed and traveling waves for a multi-type SIS epidemic model, J. Differential Equations, 229 (2006), 270-296
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C. F. Wu, P. X. Weng, Asymptotic speed of propagation and traveling wavefronts for a SIR epidemic model, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 867-892
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Z. Xu, Traveling waves in a Kermack-Mckendrick epidemic model with diffusion and latent period, Nonlinear Anal., 111 (2014), 66-81
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R. Xu, Z. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. Real World Appl., 10 (2009), 3175-3189
]
Using differentiation matrices for pseudospectral method solve Duffing Oscillator
Using differentiation matrices for pseudospectral method solve Duffing Oscillator
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en
This article presents an approximate numerical solution for nonlinear Duffing Oscillators by pseudospectral (PS) method to compare boundary conditions on the interval [-1, 1]. In the PS method, we have been used differentiation matrix for Chebyshev points to calculate numerical results for nonlinear Duffing Oscillators. The results of the comparison show that this solution had the high degree of accuracy and very small errors. The software used for the calculations in this study was Mathematica V.10.4.
1331
1336
L. A.
Nhat
L. A.
Nhat
PhD student of RUDN University
Lecture at Tan Trao University
PhD student of RUDN University
Lecture at Tan Trao University
Russia
Vietnam
Duffing oscillator
pseudospectral methods
differential matrix
Duffing system
Chebyshev points
using-differentiation-matrices-for-pseudospectral-method-solve-duffing-oscillator.pdf
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[1]
M. A. Al-Jawary, S. G. Abd-Al-Razaq, Analytic and numerical solution for duffing equations, Int. J. Basic Appl. Sci. , 5 (2016), 115-119
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B. Bulbul, M. Sezer, Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method, J. Appl. Math., 2013 (2013), 1-6
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W. S. Don, A. Solomonoff, Accuracy and speed in computing the Chebyshev collocation derivative, SIAM J. Sci. Comput., 16 (1995), 1253-1268
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A. Elias-Ziga, O. Martnez-Romero, R. K. Crdoba-Daz, Approximate Solution for the Duffing–Harmonic Oscillator by the Enhanced Cubication Method, Math. Probl. Eng., 2012 (2012), 1-12
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A. O. El-Nady, M. M. A. Lashin, Approximate Solution of Nonlinear Duffing Oscillator Using Taylor Expansion, J. Mech. Engi. Auto., 6 (2016), 110-116
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A. M. El-Naggar, G. M. Ismail , Analytical solution of strongly nonlinear Duffing Oscillators, Alex. Engi. Jour., 55 (2016), 1581-1585
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R. H. Enns, G. C. McGuire, Nonlinear Physics with Mathematica for Scientists and Engineers, Birkhauser Basel, Boston (2001)
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M. Gorji-Bandpy, M. A. Azimi, M. M. Mostofi , Analytical methods to a generalized Duffing oscillator, Australian J. Basic Appl. Sci., 5 (2011), 788-796
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M. A. Hosen, M. S. H. Chowdhury, M. Y. Ali, A. F. Ismail, An analytical approximation technique for the duffing oscillator based on the energy balance method , Ital. J. Pure Appl. Math., 37 (2017), 455-466
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H.-Y. Lin, C.-C. Yen, K.-C. Jen, K. C. Jea, A Postverification Method for Solving Forced Duffing Oscillator Problems without Prescribed Periods, J. Appl. Math., 2014 (2014), 1-10
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J. C. Mason, D. C. Handscomb, Chebyshev Polynomials, Chapman & Hall/CRC, Boca Raton, FL (2003)
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S. Nourazar, A. Mirzabeigy, Approximate solution for nonlinear Duffing oscillator with damping effect using the modified differential transform method, Scientia Iranica, 20 (2013), 364-368
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A. Saadatmandi, F. Mashhadi-Fini , A pseudospectral method for nonlinear Duffing equation involving both integral and nonintegral forcing terms, Math. Methods Appl. Sci., 38 (2015), 1265-1272
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A. H. Salas, J. E. Castillo H., Exact Solution to Duffing Equation and the Pendulum Equation, Appl. Math. Sci., 8 (2014), 8781-8789
]
Behavior analysis for a size-structured population model with Logistic term and periodic vital rates
Behavior analysis for a size-structured population model with Logistic term and periodic vital rates
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en
In this paper, we investigate the large-time behavior of a nonlinear size-structured population model with logistic term and \(T\)-periodic vital rates. We establish the existence of a unique non-negative solution of the given model with the given initial distribution. We prove that there exists at most two \(T\)-periodic non-negative solutions (one of them being the trivial one) of the periodic model associated with the given model. We show that for any initial distribution of population the solution of the given model tends to the nontrivial non-negative \(T\)-periodic solution of the associated model. At last, we
give the numerical tests, which are used to demonstrate the effectiveness of the theoretical results in our paper.
1337
1354
Rong
Liu
Rong
Liu
Shanxi University
Shanxi University
China
Guirong
Liu
Guirong
Liu
Shanxi University
Shanxi University
China
Behavior analysis
logistic term
periodic vital rates
size-structure
behavior-analysis-for-a-size-structured-population-model-with-logistic-term-and-periodic-vital-rates.pdf
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Z. Abo-Hammour, O. A. Arqub, S. Momani, N. Shawagfeh , Optimization solution of Troesch’s and Bratu’s problems of ordinary type using novel continuous genetic algorithm , Discrete Dyn. Nat. Soc., 2014 (2014), 1-15
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O. Acana, M. M. A. Qurashib, D. Baleanu, New exact solution of generalized biological population model, J. Nonlinear Sci. Appl., 10 (2017), 3916-3929
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M. Al-Smadi, O. A. Arqub, N. Shawagfeh, S. Momani, Numerical investigations for systems of second-order periodic boundary value problems using reproducing kernel method, Appl. Math. Comput., 291 (2016), 137-148
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M. Al-Smadi, A. Freihat, O. A. Arqub, N. Shawagfeh, A novel multistep generalized differential transform method for solving fractional-order Lü chaotic and hyperchaotic systems, J. Computat. Anal. Appl., 19 (2015), 713-724
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S. Aniţa, Analysis and control of age-dependent population dynamics, Kluwer Academic Publishers, Dordrecht (2000)
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L.-I. Aniţa, S. Aniţa , Note on some periodic optimal harvesting problems for age-structured population dynamics, Appl. Math. Comput., 276 (2016), 21-30
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L.-I. Aniţa, S. Aniţa, V. Arnăutu, Global behavior for age-dependent population model with logistic term and periodic vital rates, Appl. Math. Comput., 206 (2008), 368-379
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L.-I. Aniţa, S. Aniţa, V. Arnăutu, Optimal harvesting for periodic age-dependent population dynamics with logistic term, Appl. Math. Comput., 215 (2009), 2701-2715
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O. A. Arqub, An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations, J. Comput. Anal. Appl., 8 (2015), 857-874
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O. A. Arqub, Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions, Compu. Math. Appl., 73 (2017), 1243-1261
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S. Bhattacharya, M. Martcheva, Oscillation in a size-structured prey-predator model, Math. Biosci., 228 (2010), 31-44
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H. Caswell , Matrix population models: construction, analysis and interpretation, Sinauer Associations, Sunderland (2001)
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A. L. Dawidowicz, A. Poskrobko, Age-dependent single-species population dynamics with delayed argument , Math. Methods Appl. Sci., 33 (2010), 1122-1135
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A. L. Dawidowicz, A. Poskrobko, Stability of the age-dependent system with delayed dependence of the structure, Math. Methods Appl. Sci., 37 (2013), 1240-1248
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B. Ebenman, L. Persson, Size-structured populations: ecology and evolution, Springer-Verlag, Berlin (1988)
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J. Z. Farkas, T. Hagen, Asymptotic behavior of size-structured populations via juvenile-adult interaction, Discrete Contin. Dyn. Syst. Ser. B, 9 (2008), 249-266
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X. L. Fu, D. M. Zhu, Stability results for a size-structured population model with delayed birth process, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 109-131
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Z.-R. He, Y. Liu, An optimal birth control problem for a dynamical population model with size-structure, Nonlinear Anal. Real World Appl., 13 (2012), 1369-1378
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Z.-R. He, R. Liu, Theory of optimal harvesting for a nonlinear size-structured population in periodic environments, Int. J. Biomath., 7 (2014), 1-18
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M. Iannelli, Mathematical theory of age-structured population dynamics, Giardini Editori, Pisa (1995)
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N. Kato , Optimal harvesting for nonlinear size-structured population dynamics, J. Math. Anal. Appl., 342 (2008), 1388-1398
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Y. Liu, Z.-R. He , Behavioral analysis of a nonlinear three-staged population model with age-size-structure, Appl. Math. Comput., 227 (2014), 437-448
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R. Liu, G. R. Liu , Optimal birth control problems for a nonlinear vermin population model with size-structure, J. Math. Anal. Appl., 449 (2017), 265-291
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N. Shawagfeh, O. A. Arqub, S. Momani , Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method, J. Comput. Anal. Appl., 16 (2014), 750-762
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W. J. Wang, H. Feng , On the dynamics of positive solutions for the difference equation in a new population model, J. Nonlinear Sci. Appl., 9 (2016), 1748-1754
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]
Nonlinear perturbed difference equations
Nonlinear perturbed difference equations
en
en
The paper reports on an iteration algorithm to compute asymptotic solutions at any order for a wide class of nonlinear singularly perturbed difference equations.
1355
1362
Tahia
Zerizer
Tahia
Zerizer
Jazan University
Jazan University
Kingdom of Saudi Arabia
Perturbed difference equations
computational methods
boundary value problem
asymptotic expansions
iterative method
nonlinear-perturbed-difference-equations.pdf
[
]
Global existence and blow-up behavior for a degenerate and singular parabolic equation with nonlocal boundary condition
Global existence and blow-up behavior for a degenerate and singular parabolic equation with nonlocal boundary condition
en
en
The aim of this article is to investigate the global existence and blow-up behavior of the nonnegative solution to a degenerate and singular parabolic equation with nonlocal boundary condition. The conditions on the existence and non-existence of the global solution are given. Furthermore, under some appropriate hypotheses, the precise blow-up rate estimate and the uniform blow-up profile of the blow-up solutions are discussed.
1363
1373
Dengming
Liu
Dengming
Liu
Hunan University of Science and Technology
Hunan University of Science and Technology
People's Republic of China
Degenerate and singular parabolic equation
global existence
blow-up
blow-up rate
uniform blow-up profile
global-existence-and-blow-up-behavior-for-a-degenerate-and-singular-parabolic-equation-with-nonlocal-boundary-condition.pdf
[
]
The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces
The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces
en
en
Let \(K\) be a nonempty closed convex subset of a Banach space \(E\) and \(T: K\rightarrow K\) be a nonexpansive mapping. Using a viscosity approximation method, we study the implicit midpoint rule of a nonexpansive mapping \(T.\) We establish a strong convergence theorem for an iterative algorithm in the framework of uniformly smooth Banach spaces and apply our result to obtain the solutions of an accretive mapping and a variational inequality problem. The numerical example which compares the rates of convergence shows that the iterative algorithm is the most efficient. Our result is unique and the method of proof is of independent interest.
1374
1391
M. O.
Aibinu
M. O.
Aibinu
University of KwaZulu-Natal
University of KwaZulu-Natal
South Africa
P.
Pillay
P.
Pillay
University of KwaZulu-Natal
University of KwaZulu-Natal
South Africa
J. O.
Olaleru
J. O.
Olaleru
University of Lagos
University of Lagos
Nigeria
O. T.
Mewomo
O. T.
Mewomo
University of KwaZulu-Natal
University of KwaZulu-Natal
South Africa
Viscosity technique
implicit midpoint rule
nonexpansive
accretive
variational inequality problem
the-implicit-midpoint-rule-of-nonexpansive-mappings-and-applications-in-uniformly-smooth-banach-spaces.pdf
[
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