Search results for "Crank–Nicolson method"

showing 3 items of 3 documents

Operator splitting methods for American option pricing

2004

Abstract We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.

Backward differentiation formulaMathematical optimizationPartial differential equationDiscretizationApplied MathematicsFinite difference methodSemi-elliptic operatorTime discretizationValuation of optionsComplementarity theoryLinear complementarity problemCrank–Nicolson methodOperator splitting methodAmerican optionMathematicsApplied Mathematics Letters
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DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010

Mathematical analysisMathematicsofComputing_NUMERICALANALYSISNumerical methods for ordinary differential equationsExplicit and implicit methods-Backward Euler methodModeling and SimulationCollocation methodQA1-939Crank–Nicolson methodDifferential algebraic equationMathematicsAnalysisMathematicsMatrix methodNumerical partial differential equationsMathematical Modelling and Analysis
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Efficient numerical method for simulating static and dynamic properties of superfluid helium

2004

Density functional theory (DFT) offers computationally affordable way of describing static and dynamic properties of superfluid 4He. In general, the DFT models yield single particle-like Schrodinger equations with a nonlinear potential term that accounts for all the many-body interactions. The resulting equations can be solved for small amplitude plane wave excitations in the bulk whereas fully numerical solution must be sought in more complicated cases. In this paper we propose a numerical method that can be used in solving the time-dependent nonlinear Schrodinger equation in both real and imaginary times. The method is based on operator splitting technique where each component operator is…

Numerical AnalysisPhysics and Astronomy (miscellaneous)Applied MathematicsNumerical analysisOperator (physics)Plane waveComputer Science ApplicationsSchrödinger equationComputational Mathematicssymbols.namesakeNonlinear systemClassical mechanicsModeling and SimulationsymbolsCrank–Nicolson methodNonlinear Schrödinger equationSuperfluid helium-4MathematicsJournal of Computational Physics
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