Journal Article10.1007/BF02510406
A second order backward difference method with variable steps for a parabolic problem
103
TL;DR: In this paper, the numerical solution of a parabolic problem is studied and the equation is discretized in time by means of a second order two step backward difference method with variable time step.
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Abstract: The numerical solution of a parabolic problem is studied. The equation is discretized in time by means of a second order two step backward difference method with variable time step. A stability result is proved by the energy method under certain restrictions on the ratios of successive time steps. Error estimates are derived and applications are given to homogenous equations with initial data of low regularity.
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Citations
Quadratic Convergence for Valuing American Options Using a Penalty Method
Peter Forsyth,Kenneth R. Vetzal +1 more
TL;DR: The convergence of a penalty method for solving the discrete regularized American option valuation problem is studied and it is observed that an implicit treatment of the American constraint does not converge quadratically if constant timesteps are used.
A discrete Gr\"{o}nwall inequality with application to numerical schemes for subdiffusion problems
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261
A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation
TL;DR: A second order in time variable step BDF2 numerical scheme for the Cahn--Hilliard equation that relies on a second order backward difference, convex-splitting, and a third order forward difference is presented.
132
A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion
TL;DR: A semi-Lagrangian method is presented to price continuously observed fixed strike Asian options and it is observed that the nonsmoothness at the strike in the payoff affects the convergence rate; a subquadratic convergence rate is observed.
Stability and error of the variable two-step BDF for semilinear parabolic problems
TL;DR: In this paper, the temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analyzed.
References
•Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
- 01 Jan 1978
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
8.9K
•Book
Galerkin Finite Element Methods for Parabolic Problems
Vidar Thomée
- 01 Jun 1984
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
2.2K
Numerical solution of an evolution equation with a positive-type memory term
William McLean,Vidar Thomée +1 more
TL;DR: In this paper, the numerical solution of an initial-boundary value problem for a Volterra type integro-differential equation, in which the integral operator is a convolution product of a positive-definite kernel and an elliptic partial differential operator, is studied.
Stability of multistep-methods on variable grids
TL;DR: A necessary and sufficient condition for stability is given from which generalizations of recent results by Gear et al. and by Zlatev can be obtained as special cases.
116