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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2011, Volume 235, Issue 13, pp. 3728 - 3733
In this paper we present a numerical method for a generalized BlackScholes equation, which is used for option pricing. The method is based on a central... 
Piecewise uniform mesh | BlackScholes equation | Central difference scheme | Singularity | Option valuation
Journal Article
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2018, Volume 333, pp. 382 - 394
The purpose of this paper is to present a uniform finite difference method for the numerical solution of a second order singularly perturbed delay differential... 
Finite difference scheme | Error estimates | Piecewise-uniform mesh | Delay differential equation | Singular perturbation | SCHEME | MATHEMATICS, APPLIED | SYSTEMS | LAYER BEHAVIOR | SHIFTS | Analysis | Methods | Differential equations
Journal Article
ADVANCES IN DIFFERENCE EQUATIONS, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 14
Journal Article
Discrete Dynamics in Nature and Society, ISSN 1026-0226, 5/2019, Volume 2019, pp. 1 - 11
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2018, Volume 336, pp. 1 - 7
In this paper a two-point boundary value problem with a Caputo fractional derivative is considered. By using a shooting method based on the secant iterative... 
integral–differential equation | Boundary value problem | Shooting method | Caputo fractional derivative | Convergence analysis | MATHEMATICS, APPLIED | integral-differential equation | CALCULUS | EQUATIONS | Methods | Differential equations
Journal Article
Mathematical Problems in Engineering, ISSN 1024-123X, 3/2014, Volume 2014, pp. 1 - 7
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2017, Volume 315, pp. 445 - 452
This paper is devoted to giving a rigorous numerical analysis for a fractional differential equation with order α ∈ (0, 1). First the fractional differential... 
Fractional differential equation | Adapted mesh | Volterra integral equation | Caputo fractional derivative | Convergence analysis | MATHEMATICS, APPLIED | TIME RANDOM-WALKS | SPLINE COLLOCATION | BOUNDARY-VALUE-PROBLEMS | Numerical analysis | Analysis | Methods | Differential equations
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 04/2018, Volume 75, Issue 8, pp. 2874 - 2887
In this paper a time-fractional Black–Scholes equation is examined. We transform the initial value problem into an equivalent integral–differential equation... 
Fractional differential equation | Singularity | Adapted mesh | Black–Scholes equation | Option valuation | AMERICAN | MATHEMATICS, APPLIED | FINITE-VOLUME METHOD | SPLINE COLLOCATION | ERROR ANALYSIS | Black-Scholes equation | DOUBLE-BARRIER OPTIONS | Analysis | Differential equations
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2017, Volume 320, pp. 176 - 192
A second-order initial value problem with a small parameter multiplying the first- and second-order derivatives is considered. The precise knowledge about the... 
Uniform convergence | Difference scheme | Shishkin mesh | Singular perturbation | Initial value problem | SYSTEM | Uhiform convergence | MATHEMATICS, APPLIED | NUMERICAL-METHOD | BOUNDARY-VALUE-PROBLEMS
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 04/2019, Volume 90, pp. 79 - 85
A reaction–diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the... 
Fractional differential equation | Singularity | Graded mesh | Caputo derivative | MATHEMATICS, APPLIED
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2008, Volume 221, Issue 1, pp. 174 - 182
In this paper we consider a singularly perturbed quasilinear boundary value problem depending on a parameter. The problem is discretized using a hybrid... 
Uniform convergence | Parameterized problem | Midpoint difference scheme | Singular perturbation | Shishkin meshes | MATHEMATICS, APPLIED | Singular perturbations | Parameterized problems
Journal Article
Journal of Number Theory, ISSN 0022-314X, 11/2017, Volume 180, pp. 360 - 372
Let r≠0 and s≠0 be two given real numbers. Chen [7] (2016) obtained recursive relation for determining the coefficients aj(r,s) such... 
Euler–Mascheroni constant | Cycle indicator polynomial | Asymptotic expansion | Psi function | GENERATED APPROXIMATION | MATHEMATICS | Euler-Mascheroni constant | INEQUALITIES | SERIES | GAMMA FUNCTION | GENERALIZED STIRLING FORMULA
Journal Article
Environmental Pollution, ISSN 0269-7491, 11/2018, Volume 242, Issue Pt B, pp. 1266 - 1273
Ambient ozone is one of the most important air pollutants with respect to its impacts on human health and its increasing concentrations globally. However,... 
Ozone | Economic loss estimation | Chronic obstructive pulmonary disease | Years of life lost | SOUTHERN CHINA | METRICS | CITIES | AMBIENT AIR-POLLUTION | ENVIRONMENTAL SCIENCES | PREMATURE MORTALITY | DAILY MORTALITY | HEALTH | ASSOCIATION | EXPOSURE | COPD | Medical research | Lung diseases, Obstructive | Analysis | Environmental aspects | Medicine, Experimental | Air pollution | Rivers
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2015, Volume 252, pp. 229 - 239
In this paper we apply a hybrid finite difference scheme to evaluate the prices of Asian call options with fixed strike price. We use the Crank–Nicolson method... 
Central difference method | Midpoint upwind scheme | Asian option | Partial differential equation | Crank–Nicolson method | Crank-Nicolson method | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | Pricing | Operators | Approximation | Discretization | Mathematical analysis | Mathematical models | Asian | Strikes | Finite difference method
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2013, Volume 224, pp. 719 - 723
Divided differences is a very important tool, often used both in theory and in practice, for the approximation of functions. In this paper, we employ divided... 
Divided difference | Two-term recurrence | Complete Bell polynomial | Faà di Bruno’s formula | Bruno's formula | Faà di | Bell polynomial | Complete | Q-ANALOG | POLYNOMIALS | MATHEMATICS, APPLIED | LAGRANGE | Faa di Bruno's formula | STIRLING NUMBERS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2005, Volume 169, Issue 1, pp. 689 - 699
A singularly perturbed convection diffusion problem with a discontinuous convection coefficient is considered. Due to the discontinuity an interior layer... 
Convection diffusion | Shishkin mesh | Singularly perturbed | Hybrid difference scheme | MATHEMATICS, APPLIED | singularly perturbed | convection diffusion | hybrid difference scheme
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2013, Volume 219, Issue 16, pp. 8667 - 8675
► We propose a stable finite difference scheme for pricing Asian call options. ► The scheme combines a central difference scheme on a moving mesh with... 
Path-dependent option | Finite difference | Moving mesh method | Asian option | Rannacher time stepping scheme | AMERICAN | MATHEMATICS, APPLIED | VOLUME METHOD | Pricing
Journal Article
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