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High-order accurate variable time step compact schemes for pricing vanilla and exotic options
In this paper, a fourth order accurate variable time step compact scheme is developed for pricing vanilla and exotic options. Variable time step...
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Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations
This work is concerned with numerical analysis of the variable-step time filtered backward Euler scheme (see e.g. DeCaria in SIAM J Sci Comput...
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Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model
A fully implicit numerical scheme is established for solving the time fractional Swift-Hohenberg equation with a Caputo time derivative of order
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Adaptive Time Step Methods
In practical computations, one seeks to achieve a desired accuracy with the minimum computational effort. For a given method, this requires finding...
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The variable two-step BDF method for parabolic equations
The two-step backward difference formula (BDF) method on variable grids for parabolic equations with self-adjoint elliptic part is considered....
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Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-step** schemes...
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Convergence and Superconvergence Analysis of a Nonconforming Finite Element Variable-Time-Step BDF2 Implicit Scheme for Linear Reaction-Diffusion Equations
In this paper, an effective fully-discrete implicit scheme for solving linear reaction-diffusion equations is constructed by using the...
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Three-Level Schemes with Double Change in the Time Step
AbstractNonstationary problems are solved numerically by applying multilevel (with more than two levels) time approximations. They are easy to...
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A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations
This paper develops a generalized scalar auxiliary variable (SAV) method for the time-dependent Ginzburg-Landau equations. The backward Euler method...
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Comparison of implicit–explicit and Newton linearized variable two-step BDF methods for semilinear parabolic equations
It is interesting to compare implicit–explicit (IMEX) and Newton linearized (NL) methods since they are two classes of typical time discretization...
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Accelerating Explicit Time-Step** with Spatially Variable Time Steps Through Machine Learning
Use of machine learning (ML) to solve partial differential equations (PDEs) is a growing area of research. In this work we apply ML to accelerate a...
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Space-time pseudospectral method for the variable-order space-time fractional diffusion equation
In this paper, we study the space-time variable-order fractional diffusion equation with a variable diffusion coefficient. The fractional derivatives...
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An efficient algorithm for solving the variable-order time-fractional generalized Burgers’ equation
A numerical scheme based on the Haar wavelets coupled with the nonstandard finite difference scheme is presented to solve the variable-order...
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A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems
The approximate solution to second-order Hamiltonian and stiff differential systems is obtained using an efficient hybrid Nyström method (HNM) in...
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A class of monotonicity-preserving variable-step discretizations for Volterra integral equations
We study in this paper the monotonicity properties of the numerical solutions to Volterra integral equations with nonincreasing completely positive...
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A weighted ADI scheme with variable time steps for diffusion-wave equations
We study a weighted alternating direction implicit (ADI) numerical method with variable time steps for two-dimensional diffusion-wave equations. The...
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Variable-step deferred correction methods based on backward differentiation formulae for ordinary differential equations
This paper presents a sequence of variable time step deferred correction (DC) methods constructed recursively from the second-order backward...
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Numerical Analysis of a Convex-Splitting BDF2 Method with Variable Time-Steps for the Cahn–Hilliard Model
In this paper, the convex-splitting BDF2 method with variable time-steps (proposed in Chen et al. SIAM J Numer Anal 57:495–525, 2019) is reconsidered...
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Consensus Strategies for a Hegselmann–Krause Model with Leadership and Time Variable Time Delay
We analyze Hegselmann-Krause opinion formation models with leadership in presence of time delay effects. In particular, we consider a model with a...
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A fast finite difference method for 2D time variable fractional mobile/immobile equation
In this paper, we establish a fast Crank–Nicolson L1 finite difference scheme for two-dimensional time variable fractional mobile/immobile diffusion...
