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An Accurate Compact Finite Difference Scheme for Solving the American Option with M-Regime Switching Model
American option prices with M -regime switching satisfy a system of M free boundary value problems, which is challenging to solve, particularly for...
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Maximum-Norm Error Estimates of Fourth-Order Compact and ADI Compact Finite Difference Methods for Nonlinear Coupled Bacterial Systems
In this paper, by introducing two temporal derivative-dependent auxiliary variables, a linearized and decoupled fourth-order compact finite...
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Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations
In this paper, two efficient, linearized (or semi-implicit) Crank-Nicolson block-centered finite difference algorithms for the strongly nonlinear...
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Analysis of a Narrow-Stencil Finite Difference Method for Approximating Viscosity Solutions of Fully Nonlinear Second Order Parabolic PDEs
This paper approximates viscosity solutions of fully nonlinear second order parabolic PDEs by a narrow-stencil finite difference...
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Uniformly convergent finite difference methods for singularly perturbed parabolic partial differential equations with mixed shifts
In this paper, exponentially fitted finite difference methods are presented for singularly perturbed one-dimensional parabolic partial differential...
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Numerical solution of time dependent nonlinear partial differential equations using a novel block method coupled with compact finite difference schemes
In this paper, we have developed a novel three step second derivative block method and coupled it with fourth order standard compact finite...
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High-order bounds-satisfying approximation of partial differential equations via finite element variational inequalities
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite...
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Galerkin spectral and finite difference methods for the solution of fourth-order time fractional partial integro-differential equation with a weakly singular kernel
In this paper, we propose an efficient numerical algorithm for the solution of fourth-order time fractional partial integro-differential equation...
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Second-order finite difference approximation for a nonlinear size-structured population model with an indefinite growth rate coupled with the environment
In this article we develop a second-order high resolution finite difference method for a general size-structured population model coupled with...
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High Order Finite Difference WENO Methods for Shallow Water Equations on Curvilinear Meshes
A high order finite difference numerical scheme is developed for the shallow water equations on curvilinear meshes based on an alternative flux...
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Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes
This paper considers the finite difference (FD) approximations of diffusion operators and the boundary treatments for different boundary conditions....
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Numerical analysis of a linear second-order finite difference scheme for space-fractional Allen–Cahn equations
In this paper, we construct a new linear second-order finite difference scheme with two parameters for space-fractional Allen–Cahn equations. We...
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A class of second-order and dynamically consistent nonstandard finite difference schemes for nonlinear Volterra’s population growth model
In a recent work (Hoang in Math Comput Simul 199:359–373, 2022), a class of nonstandard finite difference (NSFD) schemes preserving the positivity...
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Positivity-preserving finite volume difference schemes for atmospheric dispersion models with degenerate vertical diffusion
Finite volume fitted difference schemes are constructed for one and two-dimensional air-pollution models with degenerate vertical diffusion. A weak...
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A Non-Stiff Summation-By-Parts Finite Difference Method for the Scalar Wave Equation in Second Order Form: Characteristic Boundary Conditions and Nonlinear Interfaces
Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate...
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A Stabilized Difference Finite Element Method for the 3D Steady Incompressible Navier-Stokes Equations
In this paper, we develop a stabilized difference finite element (SDFE) method for the 3D steady incompressible Navier-Stokes equations and apply...
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A radial basis function-Hermite finite difference (RBF-HFD) method for the cubic-quintic complex Ginzburg–Landau equation
In this paper, the cubic–quintic complex Ginzburg–Landau (CQCGL) equation is numerically studied in 1D, 2D and 3D spaces. First, by the Strang...
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Comparative Analysis of the Matrix Method and the Finite-Difference Method for Modeling the Distribution of Minority Charge Carriers in a Multilayer Planar Semiconductor Structure
The stationary differential heat and mass transfer equation with discontinuous coefficients describes various time-independent physical processes,...
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Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation
In this paper, two fourth-order compact finite difference schemes are derived to solve the nonlinear fourth-order wave equation which can be viewed...
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