An ETD Crank-Nicolson method for reaction-diffusion systems (Q2910812)
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scientific article; zbMATH DE number 6081137
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An ETD Crank-Nicolson method for reaction-diffusion systems |
scientific article; zbMATH DE number 6081137 |
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An ETD Crank-Nicolson method for reaction-diffusion systems (English)
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11 September 2012
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exponential time Runge-Kutta method
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reaction-diffusion equation
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convergence
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initial damping
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chemotaxis
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exotic options
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exponential time differencing
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nonlinear Black-Scholes equation
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transaction cost
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Crank-Nicolson-method
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stability
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The authors propose the exponential time difference Crank-Nicolson-(ETD-CN)-method for a class of reaction-diffusion problems. The convergence and stability are proved and illustrated for partial differential equations (PDEs) with smooth initial values. For PDEs with nonsmooth initial values and nonlinear transaction cost, for instance the chemotaxis and exotic options, the authors show the efficiency and second-order numerical convergence of the ETD-CN scheme when the initial damping technique is used.
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