An ETD Crank-Nicolson method for reaction-diffusion systems

DOI10.1002/num.20682zbMath1253.65128OpenAlexW2130213491MaRDI QIDQ2910812

B. Kleefeld, Bruce A. Wade, Abdul Q. M. Khaliq

Publication date: 11 September 2012

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20682

zbMATH Keywords

stabilityconvergencechemotaxisreaction-diffusion equationtransaction costexotic optionsexponential time differencingnonlinear Black-Scholes equationCrank-Nicolson-methodexponential time Runge-Kutta methodinitial damping

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (28)

Exponential time differencing Crank-Nicolson method with a quartic spline approximation for nonlinear Schrödinger equations ⋮ Numerical approach for a class of distributed order time fractional partial differential equations ⋮ Array-representation integration factor method for high-dimensional systems ⋮ Semi-implicit integration factor methods on sparse grids for high-dimensional systems ⋮ Fully discretized energy stable schemes for hydrodynamic equations governing two-phase viscous fluid flows ⋮ Numerical approximation of nonlinear fractional parabolic differential equations with Caputo-Fabrizio derivative in Riemann-Liouville sense ⋮ Time discretization and stability regions for dissipative-dispersive Kuramoto-Sivashinsky equation arising in turbulent gas flow over laminar liquid ⋮ Partial differential integral equation model for pricing American option under multi state regime switching with jumps ⋮ A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting ⋮ Second-order time integrators with the Fourier spectral method in application to multidimensional space-fractional Fitzhugh-Nagumo model ⋮ PRICING AMERICAN OPTION USING A MODIFIED FRACTIONAL BLACK–SCHOLES MODEL UNDER MULTI-STATE REGIME SWITCHING ⋮ Compact implicit integration factor methods for a family of semilinear fourth-order parabolic equations ⋮ Traveling Waves and Pattern Formation for Spatially Discrete Bistable Reaction-Diffusion Equations ⋮ Solving complex PDE systems for pricing American options with regime‐switching by efficient exponential time differencing schemes ⋮ The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost ⋮ Linearly implicit predictor-corrector methods for space-fractional reaction-diffusion equations with non-smooth initial data ⋮ Solving complex PIDE systems for pricing American option under multi-state regime switching jump-diffusion model ⋮ Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations ⋮ Exponential integrator methods for systems of non-linear space-fractional models with super-diffusion processes in pattern formation ⋮ Krylov integration factor method on sparse grids for high spatial dimension convection-diffusion equations ⋮ Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations ⋮ A real distinct poles exponential time differencing scheme for reaction-diffusion systems ⋮ Pricing American options under multi-state regime switching with an efficientL- stable method ⋮ Nonoverlapping localized exponential time differencing methods for diffusion problems ⋮ Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction-diffusion equations ⋮ The locally extrapolated exponential time differencing LOD scheme for multidimensional reaction-diffusion systems ⋮ Efficient time discretization scheme for nonlinear space fractional reaction–diffusion equations ⋮ A second-order efficientL-stable numerical method for space fractional reaction–diffusion equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Pricing of Options and Corporate Liabilities
• Exponential time differencing for stiff systems
• On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options
• Finite element solution of diffusion problems with irregular data
• Semigroups of linear operators and applications to partial differential equations
• Option pricing with transaction costs and a nonlinear Black-Scholes equation
• Exponential Runge-Kutta methods for parabolic problems.
• On the Hoggard-Whalley-Wilmott equation for the pricing of options with transaction costs
• Efficient semi-implicit schemes for stiff systems
• Analysis and applications of the exponential time differencing schemes and their contour integration modifications
• Incomplete Iterations in Multistep Backward Difference Methods for Parabolic Problems with Smooth and Nonsmooth Data
• On the smoothing property of the crank-nicolson scheme
• Kombinationswirbelfelder in realen Strömungen
• A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems
• Smoothing properties and approximation of time derivatives for parabolic equations: constant time steps
• Smoothing with positivity-preserving Padé schemes for parabolic problems with nonsmooth data
• High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation
• Fourth-Order Time-Stepping for Stiff PDEs
• High order smoothing schemes for inhomogeneous parabolic problems with applications in option pricing
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

This page was built for publication: An ETD Crank-Nicolson method for reaction-diffusion systems