On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance

DOI10.1137/18M1194328zbMath1422.65189OpenAlexW2948777523MaRDI QIDQ5232287

Yingzi Chen, Hua Fang, Wan-Sheng Wang

Publication date: 2 September 2019

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1194328

zbMATH Keywords

stabilityerror estimatesfinite difference methodparabolic equationsjump-diffusion modelimplicit-explicit methodspartial integro-differential equationtwo-step backward differentiation formulaoptions pricing

Mathematics Subject Classification ID

Related Items (38)

Using of PQWs for solving NFID in the complex plane ⋮ Optimal a posteriori estimators for the variable step-size BDF2 method for linear parabolic equations ⋮ Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model ⋮ Sharp error estimate of an implicit BDF2 scheme with variable time steps for the phase field crystal model ⋮ Dissipativity of variable-stepsize Runge-Kutta methods for nonlinear functional differential equations with application to Nicholson's blowflies models ⋮ Some new inequalities involving \(\kappa \)-fractional integral for certain classes of functions and their applications ⋮ A variable time-step IMEX-BDF2 SAV scheme and its sharp error estimate for the Navier–Stokes equations ⋮ Multistep Runge-Kutta methods for Volterra integro-differential equations ⋮ Variable-time-step BDF2 nonconforming VEM for coupled Ginzburg-Landau equations ⋮ L^∞-norm convergence rates of an IMEX scheme for solving a partial integro-differential equation system arising from regime-switching jump-diffusion Asian option pricing ⋮ Notes on the complete elliptic integral of the first kind ⋮ A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump ⋮ Inequalities for generalized trigonometric and hyperbolic functions with one parameter ⋮ Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations ⋮ Comparison of implicit-explicit and Newton linearized variable two-step BDF methods for semilinear parabolic equations ⋮ Errors in the IMEX-BDF-OS methods for pricing American style options under the jump-diffusion model ⋮ A positivity-preserving, energy stable BDF2 scheme with variable steps for the Cahn-Hilliard equation with logarithmic potential ⋮ A novel approach of unconditional optimal error estimate of linearized and conservative Galerkin FEM for Klein-Gordon-Schrödinger equations ⋮ An improved radial basis functions method for the high-order Volterra-Fredholm integro-differential equations ⋮ Compact IMEX scheme for a moving boundary PIDE system of the regime-switching jump-diffusion Asian option pricing ⋮ Sharp rational bounds for the gamma function ⋮ An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function ⋮ Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations ⋮ Inequalities involving conformable approach for exponentially convex functions and their applications ⋮ Dynamics analysis on a class of delayed neural networks involving inertial terms ⋮ Global asymptotic stability for a nonlinear density-dependent mortality Nicholson's blowflies system involving multiple pairs of time-varying delays ⋮ Linearly implicit variable step-size BDF schemes with Fourier pseudospectral approximation for incompressible Navier-Stokes equations ⋮ Some new Hermite-Hadamard-type inequalities associated with conformable fractional integrals and their applications ⋮ Optimal two-parameter geometric and arithmetic mean bounds for the Sándor-Yang mean ⋮ A note on generalized convex functions ⋮ Some new fractional integral inequalities for exponentially \(m\)-convex functions via extended generalized Mittag-Leffler function ⋮ Hermite-Hadamard type inequalities for co-ordinated convex and qausi-convex functions and their applications ⋮ Asymptotically almost periodic dynamics on delayed Nicholson-type system involving patch structure ⋮ New Hermite-Hadamard type inequalities for \(n\)-polynomial harmonically convex functions ⋮ Unconditional error analysis of a linearized BDF2 virtual element method for nonlinear Ginzburg-Landau equation with variable time step ⋮ A posteriori error control and adaptivity for the IMEX BDF2 method for PIDEs with application to options pricing models ⋮ Second-order convergent IMEX scheme for integro-differential equations with delays arising in option pricing under hard-to-borrow jump-diffusion models ⋮ Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models

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