Abstract
For the numerical solution of initial-boundary value problems for convection-diffusion-reaction equations (2.1) the method of lines (MOL) forms a flexible and versatile approach. It is widely employed in practice and is popular in particular in computational finance. The MOL consists of two general, consecutive step.
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Bibliography
I. J. Clark, Foreign Exchange Option Pricing, Wiley, 2011.
D. J. Duffy, Finite Difference Methods in Financial Engineering, Wiley, 2006.
D. J. Higham, An Introduction to Financial Option Valuation, Cambridge Univ. Press, 2004.
W. Hundsdorfer & J. G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer, 2003.
A. R. Mitchell & D. F. Griffiths, The Finite Difference Method in Partial Differential Equations, Wiley, 1980.
G. G. O'Brien, M. A. Hyman & S. Kaplan, A study of the numerical solution of partial differential equations, J. Math. and Phys. 29 (1951) 223–251.
R. D. Richtmyer & K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed., Wiley, 1967.
R. U. Seydel, Tools for Computational Finance, 5th ed., Springer, 2012.
G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed., Clarendon Press, 1985.
M. N. Spijker, Numerical Stability, Lecture notes, Univ. Leiden, 1998.
J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth, 1989.
D. Tavella & C. Randall, Pricing Financial Instruments, Wiley, 2000.
J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, 1995.
L. N. Trefethen & M. Embree, Spectra and Pseudospectra, Princeton Univ. Press, 2005.
P. Wilmott, Derivatives, Wiley, 1999.
Y. I. Zhu, X. Wu, I. L. Chern & Z. z. Sun, Derivative Securities and Difference Methods, 2nd ed., Springer, 2013.
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in ’t Hout, K. (2017). Spatial Discretization I. In: Numerical Partial Differential Equations in Finance Explained. Financial Engineering Explained. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-137-43569-9_3
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DOI: https://doi.org/10.1057/978-1-137-43569-9_3
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