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Mathematical analysis and numerical simulation of a tumor-host model with chemotherapy application
(Communications in Mathematical Biology and Neuroscience, 2018)
In this paper, a system of non-linear quasi-parabolic partial differential system, modeling the chemotherapy application of spatial tumor-host interaction is considered. At some certain parameters, we derive the steady ...
Implicit-explicit predictor-corrector methods combined with improved spectral methods for pricing European style vanilla and exotic options
(Kent State University, 2013)
In this paper we present a robust numerical method to solve several types of European style option pricing problems. The governing equations are described by variants of Black-Scholes partial differential equations (BS-PDEs) ...
A robust spectral method for solving Heston’s model
(Springer Verlag, 2014)
In this paper, we consider the Heston’s volatility model (Heston in Rev.
Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the
spectral collocation method and the Laplace transforms method. ...
Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme
(SpringerOpen, 2016)
In this paper, we consider the numerical simulations of an extended nonlinear form
of Kierstead-Slobodkin reaction-transport system in one and two dimensions. We
employ the popular fourth-order exponential time differencing ...
A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems
(Spring Verlag, 2013)
This paper treats a time-dependent singularly perturbed reaction-diffusion problem. We semidiscretize the problem in time by means of the classical backward Euler method. We develop a fitted operator finite difference ...
Contour integral method for European options with jumps
(Elsevier, 2013)
We develop an efficient method for pricing European options with jump on a single asset. Our approach is based on the combination of two powerful numerical methods, the spectral domain decomposition method and the Laplace ...
An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection
(De Gruyter Open, 2013)
We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV
transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical ...
A robust spectral method for pricing of American put options on zero-coupon bonds
(Global-Science Press, 2018)
American put options on a zero-coupon bond problem is reformulated as a
linear complementarity problem of the option value and approximated by a nonlinear
partial differential equation. The equation is solved by an ...
Performance of Richardson extrapolation on some numerical methods for a singularly perturbed turning point problem whose solution has boundary layers
(KOREAN MATHEMATICAL SOC, 2014)
Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. ...
A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer
(Wiley, 2019)
The objective of this paper is to construct and analyzea fitted operator finite difference method (FOFDM) forthe family of time-dependent singularly perturbed parabolicconvection–diffusion problems. The solution to the ...